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Dehua Wang

Publications and source records attributed to Dehua Wang.

At least 73 records · Page 4Linked to original sources
arXiv2013

Global weak solution for a coupled compressible Navier-Stokes and Q-tensor system

In this paper, we study a coupled compressible Navier-Stokes/Q-tensor system modeling the nematic liquid crystal flow in a three-dimensional bounded spatial domain. The existence and long time dynamics of globally defined weak solutions for the coupled system are established, using weak convergence methods, compactness and interpolation arguments. The symmetry and traceless properties of the Q-tensor play key roles in this process.

math.AP↗
arXiv2013

The kHz QPOs of Neutron Stars and Millisecond Pulsars and Implications

The kilohertz quasi-periodic oscillations (kHz QPOs) have been found in neutron star low mass X-ray binaries (NS-LMXBs), which present the millisecond timing phenomena close to the surface of the compact objects. We briefly summarize the following contents: (1). The correlations and distributions of twin kHz QPOs; (2). The relations of high-low frequency QPOs; (3). The QPO properties of NS Atoll and Z sources; (4). No clear direct correlations between NS spins and QPOs; (5). The mechanisms of kHz QPOs; (6). The implications of kHZ QPOs, e.g., NS mass and radius, disk thickness and magnetic field of Atoll and Z source.

astro-ph.HE↗
arXiv2013

Global weak solutions to the inhomogeneous Navier-Stokes-Vlasov equations

A fluid-particle system of the inhomogeneous Navier-Stokes equations and Vlasov equation in the three dimensional space is considered in this paper. The coupling arises from the drag force in the fluid equations and the acceleration in the Vlasov equation. An initial-boundary value problem is studied in a bounded domain with large data. The existence of global weak solutions is established through an approximation scheme, energy estimates, and weak convergence.

math.AP↗
arXiv2013

On Multi-dimensional Compressible Flows of Nematic Liquid Crystals with Large Initial Energy in a Bounded Domain

We study the global existence of weak solutions to a multi-dimensional simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals with large initial energy in a bounded domain $Ω\subset \mathbb{R}^N$, where N=2 or 3. By exploiting a maximum principle, Nirenberg's interpolation inequality and a smallness condition imposed on the $N$-th component of initial direction field $\mf{d}_0$ to overcome the difficulties induced by the supercritical nonlinearity $|\nabla{\mathbf d}|^2{\mathbf d}$ in the equations of angular momentum, and then adapting a modified three-dimensional approximation scheme and the weak convergence arguments for the compressible Navier-Stokes equations, we establish the global existence of weak solutions to the initial-boundary problem with large initial energy and without any smallness condition on the initial density and velocity.

math.AP↗
arXiv2012

Global strong solution to the density-dependent incompressible flow of liquid crystals

The initial-boundary value problem for the density-dependent incompressible flow of liquid crystals is studied in a three-dimensional bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is established for both the local strong solution with large initial data and the global strong solution with small data. It is also proved that when the strong solution exists, a weak solution with the same data must be equal to the unique strong solution.

math.AP↗
arXiv2011

Formation of singularity for compressible viscoelasticity

The formation of singularity and breakdown of classical solutions to the three-dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solutions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.

math.AP↗
arXiv2011

Local strong solution to the compressible magnetohydrodynamic flow with large data

The three-dimensional compressible magnetohydrodynamic (MHD) isentropic flow with zero magnetic diffusivity is studied. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field. The existence and uniqueness of local in time strong solution with large initial data is established. The strong solution has weaker regularity than the classical solution. A generalized Lax-Milgram theorem and a Schauder-Tychonoff-type fixed point argument are applied with novel techniques and estimates for the strong solution.

math.AP↗
arXiv2011

Global solution to the incompressible flow of liquid crystals

The initial boundary value problem for the three-dimensional incompressible flow of liquid crystals is considered in a bounded smooth domain. The existence and uniqueness is established for both the local strong solution with large initial data and the global strong solution with small data. It is also proved that when the strong solution exists, a weak solution must be equal to the unique strong solution with the same data.

math.AP↗
arXiv2011

Incompressible limit for the compressible flow of liquid crystals

The connection between the compressible flow of liquid crystals with low Mach number and the incompressible flow of liquid crystals is studied in a bounded domain. In particular, the convergence of weak solutions of the compressible flow of liquid crystals to the weak solutions of the incompressible flow of liquid crystals is proved when the Mach number approaches zero; that is, the incompressible limit is justified for weak solutions in a bounded domain.

math.AP↗
arXiv2011

A Fluid Dynamic Formulation of the Isometric Embedding Problem in Differential Geometry

The isometric embedding problem is a fundamental problem in differential geometry. A longstanding problem is considered in this paper to characterize intrinsic metrics on a two-dimensional Riemannian manifold which can be realized as isometric immersions into the three-dimensional Euclidean space. A remarkable connection between gas dynamics and differential geometry is discussed. It is shown how the fluid dynamics can be used to formulate a geometry problem. The equations of gas dynamics are first reviewed. Then the formulation using the fluid dynamic variables in conservation laws of gas dynamics is presented for the isometric embedding problem in differential geometry.

math.AP↗
arXiv2011

Global weak solution and large-time behavior for the compressible flow of liquid crystals

The three-dimensional equations for the compressible flow of liquid crystals are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of a global weak solution are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent $γ>\frac32$.

math.AP↗
arXiv2011

The initial-boundary value problem for the compressible viscoelastic fluids

The global existence of strong solution to the initial-boundary value problem of the three-dimensional compressible viscoelastic fluids near equilibrium is established in a bounded domain. Uniform estimates in $W^{1,q}$ with $q>3$ on the density and deformation gradient are also obtained. All the results apply to the two-dimensional case.

math.AP↗
arXiv2011

Incompressible magnetohydrodynamic limit of the Vlasov-Maxwell-Boltzmann equations

The hydrodynamic limit of the Vlasov-Maxwell-Boltzmann equations is considered for weak solutions. Using relative entropy estimate about an absolute Maxwellian, an incompressible Electron-Magnetohydrodynamics-Fourier limit for solutions of the Vlasov-Maxwell-Blotzmann equations over any periodic spatial domain in $\R^3$ is studied. It is shown that any properly scaled sequence of renormalized solutions of the Vlasov-Maxwell-Boltzmann equations has fluctuations that (in the weak $L^1$ topology) converge to an infinitesimal Maxwellian with fluid variables that satisfy the incompressibility and Boussinesq relations. It is also shown that the limits of the velocity, the electric field, and the magnetic field are governed by a weak solution of an incompressible electron-magnetohydrodynamics system for all time.

math.AP↗
arXiv2011

Weak Stability and Large Time Behavior for the Cauchy Problem of the Vlasov-Maxwell-Boltzmann Equations

The Cauchy problem for the Vlasov-Maxwell-Boltzmann equations (VMB) is considered. First the renormalized solution to the Vlasov equation with the Lorentz force is discussed and the difficulty on the partial differentiability of the coefficients is overcome. Then the weak stability of the renormalized solutions to the Cauchy problem of VMB is established using the compactness of velocity averages and a renormalized formulation. Furthermore, the large time behavior of the renormalized solutions to VMB is studied and it is proved that the density of particles tends to a local Maxwellian as the time goes to infinity.

math.AP↗
arXiv2010

Global Existence for the Multi-Dimensional Compressible Viscoelastic flows

The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces. Using uniform estimates for a hyperbolic-parabolic linear system with convection terms, we prove the global existence in the Besov space which is invariant with respect to the {scaling} of the associated equations. Several important estimates are achieved, including a smoothing effect on the velocity, and the $L^1-$decay of the density and deformation gradient.

math.AP↗
arXiv2010

Strong Solutions to the Three-Dimensional Compressible Viscoelastic Fluids

The existence and uniqueness of the local strong solution to the three-dimensional compressible viscoelastic fluids near the equilibrium is established. In addition to the uniform estimates on the velocity, some essential uniform estimates on the density and the deformation gradient are also obtained.

math.AP↗
arXiv2010

Local Strong Solution to the Compressible Viscoelastic Fluid with Large Data

The existence and uniqueness of local in time strong solution with large initial data for the three-dimensional compressible viscoelastic fluid is established. The strong solution has weaker regularity than the classical solution. The Lax-Milgram theorem and the Schauder-Tychonoff fixed-point argument are applied.

math.AP↗