arXiv subjects

Dehua Wang

Publications and source records attributed to Dehua Wang.

At least 37 records · Page 2Linked to original sources

arXiv2022

Distribution of fast radio burst dispersion measures in CHIME/FRB Catalog 1: implications on the origin of FRBs

Recently, CHIME/FRB project published its first fast radio burst (FRB) catalog (hereafter, Catalog 1), which totally contains 536 unique bursts. With the help of the latest set of FRBs in this large-size catalog, we aim to investigate the dispersion measure (DM) or redshift ($z$) distribution of the FRB population, and solution of this problem could be used to clarify the question of FRB origin. In this study, we adopted the M\&E 2018 model, to fit the observed $z$ distribution of FRBs in Catalog 1. In the M\&E 2018 model, we are mostly interested in the $Φ(z)$ function, i.e., number of bursts per proper time per comoving volume, which is represented by the star formation rate (SFR) with a power-law index $n$. Our estimated value of $n$ is $0.0_{-0.0}^{+0.6}$ ($0.0_{-0.0}^{+2.1}$) at the 68 (95) per cent confidence level, implying that the FRB population evolves with redshift consistent with, or faster than, the SFR. Specially, the consistency of the $n$ values estimated by this study and the SFR provides a potential support for the hypothesis of FRBs originating from young magnetars.

astro-ph.HE↗

arXiv2022

Weak solutions to the equations of stationary compressible flows in active liquid crystals

The equations of stationary compressible flows of active liquid crystals are considered in a bounded three-dimensional domain. The system consists of the stationary Navier-Stokes equations coupled with the equation of Q-tensors and the equation of the active particles. The existence of weak solutions to the stationary problem is established through a two-level approximation scheme, compactness estimates and weak convergence arguments. Novel techniques are developed to overcome the difficulties due to the lower regularity of stationary solutions, a Moser-type iteration is used to deal with the strong coupling of active particles and fluids, and some weighted estimates on the energy functions are achieved so that the weak solutions can be constructed for all values of the adiabatic exponent $γ>1$.

math.AP↗

arXiv2022

Active Learning for Deep Visual Tracking

Convolutional neural networks (CNNs) have been successfully applied to the single target tracking task in recent years. Generally, training a deep CNN model requires numerous labeled training samples, and the number and quality of these samples directly affect the representational capability of the trained model. However, this approach is restrictive in practice, because manually labeling such a large number of training samples is time-consuming and prohibitively expensive. In this paper, we propose an active learning method for deep visual tracking, which selects and annotates the unlabeled samples to train the deep CNNs model. Under the guidance of active learning, the tracker based on the trained deep CNNs model can achieve competitive tracking performance while reducing the labeling cost. More specifically, to ensure the diversity of selected samples, we propose an active learning method based on multi-frame collaboration to select those training samples that should be and need to be annotated. Meanwhile, considering the representativeness of these selected samples, we adopt a nearest neighbor discrimination method based on the average nearest neighbor distance to screen isolated samples and low-quality samples. Therefore, the training samples subset selected based on our method requires only a given budget to maintain the diversity and representativeness of the entire sample set. Furthermore, we adopt a Tversky loss to improve the bounding box estimation of our tracker, which can ensure that the tracker achieves more accurate target states. Extensive experimental results confirm that our active learning-based tracker (ALT) achieves competitive tracking accuracy and speed compared with state-of-the-art trackers on the seven most challenging evaluation benchmarks.

cs.CV↗

arXiv2021

Weak solutions to the stationary Cahn-Hillard/Navier-Stokes equations for compressible fluids

We are concerned with the Cahn-Hilliard/Navier-Stokes equations for the stationary compressible flows in a three-dimensional bounded domain. The governing equations consist of the stationary Navier-Stokes equations describing the compressible fluid flows and the stationary Cahn-Hilliard type diffuse equation for the mass concentration difference. We prove the existence of weak solutions when the adiabatic exponent $γ$ satisfies $γ>\frac{4}{3}$. The proof is based on the weighted total energy estimates and the new techniques developed to overcome the difficulties from the capillary stress.

math.AP↗

arXiv2021

Stability of transonic contact discontinuity for two-dimensional steady compressible Euler flows in a finitely long nozzle

We consider the stability of transonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle. This is the first work on the mixed-type problem of transonic flows across a contact discontinuity as a free boundary in nozzles. We start with the Euler-Lagrangian transformation to straighten the contact discontinuity in the new coordinates. However, the upper nozzle wall in the subsonic region depending on the mass flux becomes a free boundary after the transformation. Then we develop new ideas and techniques to solve the free-boundary problem in three steps: (1) we fix the free boundary and generate a new iteration scheme to solve the corresponding fixed boundary value problem of the hyperbolic-elliptic mixed type by building some powerful estimates for both the first-order hyperbolic equation and a second-order nonlinear elliptic equation in a Lipschitz domain; (2) we update the new free boundary by constructing a mapping that has a fixed point; (3) we establish via the inverse Lagrangian coordinates transformation that the original free interface problem admits a unique piecewise smooth transonic solution near the background state, which consists of a smooth subsonic flow and a smooth supersonic flow with a contact discontinuity.

math.AP↗

arXiv2021

Inviscid Limit of Compressible Viscoelastic Equations with the No-Slip Boundary Condition

The inviscid limit for the two-dimensional compressible viscoelastic equations on the half plane is considered under the no-slip boundary condition. When the initial deformation tensor is a perturbation of the identity matrix and the initial density is near a positive constant, we establish the uniform estimates of solutions to the compressible viscoelastic flows in the conormal Sobolev spaces. It is well-known that for the corresponding inviscid limit of the compressible Navier-Stokes equations with the no-slip boundary condition, one does not expect the uniform energy estimates of solutions due to the appearance of strong boundary layers. However, when the deformation tensor effect is taken into account, our results show that the deformation tensor plays an important role in the vanishing viscosity process and can prevent the formation of strong boundary layers. As a result we are able to justify the inviscid limit of solutions for the compressible viscous flows under the no-slip boundary condition governed by the viscoelastic equations, based on the uniform conormal regularity estimates achieved in this paper.

math.AP↗

arXiv2021

Vanishing dissipation limit to the planar rarefaction wave for the three-dimensional compressible Navier-Stokes-Fourier equations

We study the vanishing dissipation limit of the three-dimensional (3D) compressible Navier-Stokes-Fourier equations to the corresponding 3D full Euler equations. Our results are twofold. First, we prove that the 3D compressible Navier-Stokes-Fourier equations admit a family of smooth solutions that converge to the planar rarefaction wave solution of the 3D compressible Euler equations with arbitrary strength. Second, we obtain a uniform convergence rate in terms of the viscosity and heat-conductivity coefficients. For this multi-dimensional problem, we first need to introduce the hyperbolic wave to recover the physical dissipations of the inviscid rarefaction wave profile as in our previous work [29] on the two-dimensional (2D) case. However, due to the 3D setting that makes the analysis significantly more challenging than the 2D problem, the hyperbolic scaled variables for the space and time could not be used to normalize the dissipation coefficients as in the 2D case. Instead, the analysis of the 3D case is carried out in the original non-scaled variables, and consequently the dissipation terms are more singular compared with the 2D scaled case. Novel ideas and techniques are developed to establish the uniform estimates. In particular, more accurate {\it a priori} assumptions with respect to the dissipation coefficients are crucially needed for the stability analysis, and some new observations on the cancellations of the physical structures for the flux terms are essentially used to justify the 3D limit. Moreover, we find that the decay rate with respect to the dissipation coefficients is determined by the nonlinear flux terms in the original variables for the 3D limit in this paper, but fully determined by the error terms in the scaled variables for the 2D case in [29].

math.AP↗

arXiv2020

Large Time Behavior and Diffusion Limit for a System of Balance Laws From Chemotaxis in Multi-dimensions

We consider the Cauchy problem for a system of balance laws derived from a chemotaxis model with singular sensitivity in multiple space dimensions. Utilizing energy methods, we first prove the global well-posedness of classical solutions to the Cauchy problem when only the energy of the first order spatial derivatives of the initial data is sufficiently small, and the solutions are shown to converge to the prescribed constant equilibrium states as time goes to infinity. Then we prove that the solutions of the fully dissipative model converge to those of the corresponding partially dissipative model when the chemical diffusion coefficient tends to zero.

math.AP↗

arXiv2020

Stationary Cahn-Hilliard-Navier-Stokes equations for the diffuse interface model of compressible flows

A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations consist of the stationary Navier-Stokes equations for compressible fluids and a stationary Cahn-Hilliard type equation for the mass concentration difference. Approximate solutions are constructed through a two-level approximation procedure, and the limit of the sequence of approximate solutions is obtained by a weak convergence method. New ideas and estimates are developed to establish the existence of weak solutions with a wide range of adiabatic exponent.

math.AP↗

arXiv2020

A Kato-type criterion for vanishing viscosity near the Onsager's critical regularity

We consider a vanishing viscosity sequence of weak solutions of the three-dimensional Navier--Stokes equations on a bounded domain. In a seminal paper [25] Kato showed that for sufficiently regular solutions, the vanishing viscosity limit is equivalent to having vanishing viscous dissipation in a boundary layer of width proportional to the viscosity. We prove that Kato's criterion holds for Hölder continuous solutions with the regularity index arbitrarily close to the Onsager's critical exponent through a new boundary layer foliation and a global mollification.

math.AP↗

arXiv2020

Global regularity of the three-dimensional fractional micropolar equations

The global well-posedness of the smooth solution to the three-dimensional (3D) incompressible micropolar equations is a difficult open problem. This paper focuses on the 3D incompressible micropolar equations with fractional dissipations $( Δ)^αu$ and $(-Δ)^βw$.Our objective is to establish the global regularity of the fractional micropolar equations with the minimal amount of dissipations. We prove that, if $α\geq \frac{5}{4}$, $β\geq 0$ and $α+β\geq\frac{7}{4}$, the fractional 3D micropolar equations always possess a unique global classical solution for any sufficiently smooth data. In addition, we also obtain the global regularity of the 3D micropolar equations with the dissipations given by Fourier multipliers that are logarithmically weaker than the fractional Laplacian.

math.AP↗

arXiv2020

Magnetic effects on the solvability of 2D MHD boundary layer equations without resistivity in Sobolev spaces

In this paper, we are concerned with the magnetic effect on the Sobolev solvability of boundary layer equations for the 2D incompressible MHD system without resistivity. The MHD boundary layer is described by the Prandtl type equations derived from the incompressible viscous MHD system without resistivity under the no-slip boundary condition on the velocity. Assuming that the initial tangential magnetic field does not degenerate, a local-in-time well-posedness in Sobolev spaces is proved without the monotonicity condition on the velocity field. Moreover, we show that if the tangential magnetic field shear layer is degenerate at one point, then the linearized MHD boundary layer system around the shear layer profile is ill-posed in the Sobolev settings provided that the initial velocity shear flow is non-degenerately critical at the same point.

math.AP↗

arXiv2020

Nonlinear stability and existence of vortex sheets for inviscid liquid-gas two-phase flow

We are concerned with the vortex sheet solutions for the inviscid two-phase flow in two dimensions. In particular, the nonlinear stability and existence of compressible vortex sheet solutions under small perturbations are established by using a modification of the Nash-Moser iteration technique, where a priori estimates for the linearized equations have a loss of derivatives. Due to the jump of the normal derivatives of densities of liquid and gas, we obtain the normal estimates in the anisotropic Sobolev space, instead of the usual Sobolev space. New ideas and techniques are developed to close the energy estimates and derive the tame estimates for the two-phase flows.

math.AP↗

arXiv2019

Well-posedness of nonisentropic Euler equations with physical vacuum

We consider the local well-posedness of the one-dimensional nonisentropic Euler equations with moving physical vacuum boundary condition. The physical vacuum singularity requires the sound speed to be scaled as the square root of the distance to the vacuum boundary. The main difficulty lies in the fact that the system of hyperbolic conservation laws becomes characteristic and degenerate at the vacuum boundary. Our proof is based on an approximation of the Euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term. Then we construct the solutions to this degenerate parabolic problem and establish the estimates that are uniform with respect to the artificial viscosity parameter. Solutions to the compressible Euler equations are obtained as the limit of the vanishing artificial viscosity. Different from the isentropic case \cite{Coutand4, Lei}, our momentum equation of conservation laws has an extra term $p_{S}S_x$ that leads to some extra terms in the energy function and causes more difficulties even for the case of $γ=2$. Moreover, we deal with this free boundary problem starting from the general cases of $2\leqγ<3$ and $1<γ<2 $ instead of only emphasizing the isentropic case of $γ=2$ in \cite{Coutand4, jang1, Lei}.

math.AP↗

arXiv2019

Global well-posedness and optimal large-time behavior of strong solutions to the non-isentropic particle-fluid flows

In this paper, we study the three-dimensional non-isentropic compressible fluid-particle flows. The system involves coupling between the Vlasov-Fokker-Planck equation and the non-isentropic compressible Navier-Stokes equations through momentum and energy exchanges. For the initial data near the given equilibrium we prove the global well-posedness of strong solutions and obtain the optimal algebraic rate of convergence in the three-dimensional whole space. For the periodic domain the same global well-posedness result still holds while the convergence rate is exponential. %The proof is based on the new macro-micro decomposition and energy estimates. New ideas and techniques are developed to establish the well-posedness and large-time behavior. For the global well-posedness our methods are based on the new macro-micro decomposition and fine energy estimates, while the proofs of the optimal large-time behavior rely on the Fourier analysis of the linearized Cauchy problem and the energy-spectrum method.

math.AP↗

arXiv2019

Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional compressible Navier-Stokes equations

The vanishing viscosity limit of the two-dimensional (2D) compressible isentropic Navier-Stokes equations is studied in the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. It is proved that there exists a family of smooth solutions for the 2D compressible Navier-Stokes equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficients away from the initial time. In the proof, the hyperbolic wave is crucially introduced to recover the physical viscosities of the inviscid rarefaction wave profile, in order to rigorously justify the vanishing viscosity limit.

math.AP↗

arXiv2018

Linear Stability of Compressible Vortex Sheets in 2D Elastodynamics: Variable Coefficients

The linear stability with variable coefficients of the vortex sheets for the two-dimensional compressible elastic flows is studied. As in our earlier work on the linear stability with constant coefficients, the problem has a free boundary which is characteristic, and also the Kreiss-Lopatinskii condition is not uniformly satisfied. In addition, the roots of the Lopatinskii determinant of the para-linearized system may coincide with the poles of the system. Such a new collapsing phenomenon causes serious difficulties when applying the bicharacteristic extension method. Motivated by our method introduced in the constant-coefficient case, we perform an upper triangularization to the para-linearized system to separate the outgoing mode into a closed form where the outgoing mode only appears at the leading order. This procedure results in a gain of regularity for the outgoing mode which allows us to overcome the loss of regularity of the characteristic components at the poles, and hence to close all the energy estimates. We find that, analogous to the constant coefficient case, elasticity generates notable stabilization effects, and there are additional stable subsonic regions compared with the isentropic Euler flows. Moreover, since our method does not rely on the construction of the bicharacterisic curves, it can also be applied to other fluid models such as the non-isentropic Euler equations and the MHD equations.

math.AP↗

arXiv2018

Energy equality in compressible fluids with physical boundaries

We study the energy balance for weak solutions of the three-dimensional compressible Navier--Stokes equations in a bounded domain. We establish an $L^p$-$L^q$ regularity conditions on the velocity field for the energy equality to hold, provided that the density is bounded and satisfies $\sqrtρ \in L^\infty_t H^1_x$. The main idea is to construct a global mollification combined with an independent boundary cut-off, and then take a double limit to prove the convergence of the resolved energy.

math.AP↗