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Huanyao Wen

Publications and source records attributed to Huanyao Wen.

At least 19 recordsLinked to original sources
arXiv2026

Vanishing capillary limit for compressible Navier-Stokes-Korteweg system in a bounded interval with large initial data

In this paper, we study vanishing capillary limit for isentropic compressible Navier-Stokes-Korteweg system in a bounded interval. The main challenges focus on the capillary term and the boundary effect. A new uniform dissipative estimate in terms of the third-order derivative of density and some correctors are derived to handle such difficulties. It leads to the optimal convergence rate of the solutions in $L^\infty$ norm globally in time with arbitrarily large initial data. This work provides a rigorous derivation of the isentropic compressible Navier-Stokes system in a bounded interval from the isentropic compressible Navier-Stokes-Korteweg system via vanishing capillary limit.

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arXiv2026

The small Deborah number limit for the compressible fluid-particle flows

In this paper, we consider the hydrodynamic limit for the fluid-particle flows governed by the Vlasov-Fokker-Planck equation coupled with the compressible Navier-Stokes equation as the Deborah number tends to zero. The proof is based on a formal derivation via the Hilbert expansion around the limiting system, the rigorous justification of which is completed by the refined energy estimates involving the macro-micro decomposition. Compared with the existing results obtained by the relative entropy argument ([A. Mellet and A. F. Vasseur, Comm. Math. Phys., 281 (2008), pp. 573-596]), the present work extends to a pointwise convergence of the hydrodynamic limits with an explicit rate for the fluid-particle coupled model.

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arXiv2026

Optimal time-decay estimates for an Oldroyd-B model with zero viscosity

In this work, we consider the Cauchy problem for a diffusive Oldroyd-B model in three dimensions. Some optimal time-decay rates of the solutions are derived via analysis of upper and lower time-decay estimates provided that the initial data are small and that the absolute value of Fourier transform of the initial velocity is bounded below away from zero in a low-frequency region. It is worth noticing that the optimal rates are independent of the fluid viscosity or the diffusive coefficient, which is a different phenomenon from that for incompressible Navier-Stokes equations.

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arXiv2026

Global well-posedness of 3D two-fluid type model with vacuum: smallness on scaling invariant quantity

This paper focuses on Cauchy problem for the three-dimensional two-fluid type model, in which the presence of vacuum is permitted. Under some assumptions that the initial data satisfy appropriate regularity conditions and a compatibility constraint, and that the newly introduced scaling-invariant initial quantities $\bar P^{\frac{ 3}γ} \left(\|\sqrt{ρ_0}u_0\|_{L^2}^2+\|P_0\|_{L^1}\right) \left(\|\nabla u_0\|_{L^2}^2+\|P_0\|_{L^2}^2\right)$ and $\bar P^{\frac{6}γ+1} \left(\|\sqrt{ρ_0}u_0\|_{L^2}^2+\|P_0\|_{L^1}\right)^3 \left(\|\nabla u_0\|_{L^2}^2+\|P_0\|_{L^2}^2\right)$ are sufficiently small, the global well-posedness of strong solutions to the two-fluid type model is derived.

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arXiv2023

The vanishing diffusion limit for an Oldroyd-B model in $\mathbb{R}^2_+$

We consider the initial-boundary value problem for an incompressible Oldroyd-B model with stress diffusion in two-dimensional upper half plane which describes the motion of viscoelastic polymeric fluids. From the physical point of view, the diffusive coefficient is several orders of magnitude smaller than other parameters in the model, and is usually assumed to be zero. However, the link between the diffusive model and the standard one (zero diffusion) via vanishing diffusion limit is still unknown from the mathematical point of view, in particular for the problem with boundary. Some numerical results [13] suggest that this should be true. In this work, we provide a rigorous justification for the vanishing diffusion in $L^\infty$-norm.

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arXiv2022

The Cauchy problem for an inviscid and non-diffusive Oldroyd-B model in two dimensions

A two-dimensional inviscid and diffusive Oldroyd-B model was investigated by [T. M. Elgindi, F. Rousset, Commun. Pure Appl. Math. 68 (2015), 2005--2021] where the global existence and uniqueness of the strong solution were established for arbitrarily large initial data. As pointed out by [A. V. Bhave, R. C. Armstrong, R. A. Brown, J. Chem. Phys. 95(1991), 2988--3000], the diffusion coefficient is significantly smaller than other effects, it is interesting to study the non-diffusive model. In the present work, we obtain the global-in-time existence and uniqueness of the strong solution to the non-diffusive model with small initial data via deriving some uniform regularity estimates and taking vanishing diffusion limits. In addition, the large time behavior of the solution is studied and the optimal time-decay rates for each order of spatial derivatives are obtained. The main challenges focus on the lack of dissipation and regularity effects of the system and on the slower decay in the two-dimensional settings. A combination of the spectral analysis and the Fourier splitting method is adopted.

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arXiv2021

On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions

We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants Γ,γ>=9/5. The pressure functions are of two components solving the continuity equations. Two typical cases for the pressure are considered, which are motivated by the compressible two-fluid model with possibly unequal velocities [3] and by a limiting system from the Vlasov-Fokker-Planck/compressible Navier-Stokes system [27] (see also some other relevant models like compressible MHD system for two-dimensional case [24] and compressible Oldroyd-B model with stress diffusion [1]). The lack of enough regularity for the two densities turns out some essential difficulties in the two-component pressure compared with the single-phase model, i.e., compressible Navier-Stokes equations. In this paper, the global existence theory does not require any domination conditions for the initial densities, which implies that transition to each single-phase flow is allowed.

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arXiv2021

The Cauchy problem for an inviscid Oldroyd-B model in $\mathbb{R}^3$

In this paper, we consider the Cauchy problem for an inviscid compressible Oldroyd-B model in three dimensions. The global well posedness of strong solutions and the associated time-decay estimates in Sobolev spaces are established near an equilibrium state. The vanishing of viscosity is the main challenge compared with our previous work [47] where the viscosity coefficients are included and the decay rates for the highest-order derivatives of the solutions seem not optimal. One of the main objectives of this paper is to develop some new dissipative estimates such that the smallness of the initial data and decay rates are independent of the viscosity. In addition, it proves that the decay rates for the highest-order derivatives of the solutions are optimal. Our proof relies on Fourier theory and delicate energy method. This work can be viewed as an extension of [47].

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arXiv2017

Global weak solution to the viscous two-fluid model with finite energy

In this paper, we prove the existence of global weak solutions to the compressible two-fluid Navier-Stokes equations in three dimensional space. The pressure depends on two different variables from the continuity equations. We develop an argument of variable reduction for the pressure law. This yields to the strong convergence of the densities, and provides the existence of global solutions in time, for the compressible two-fluid Navier-Stokes equations, with large data in three dimensional space.

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arXiv2017

Global solutions to the three-dimensional full compressible Navier-Stokes equations with vacuum at infinity in some classes of large data

We consider the Cauchy problem for the full compressible Navier-Stokes equations with vanishing of density at infinity in R3. Our main purpose is to prove the existence (and uniqueness) of global strong and classical solutions and study the large-time behavior of the solutions as well as the decay rates in time. Our main results show that the strong solution exists globally in time if the initial mass is small for the fixed coefficients of viscosity and heat conduction, and can be large for the large coefficients of viscosity and heat conduction. Moreover, large-time behavior and a surprisingly exponential decay rate of the strong solution are obtained. Finally, we show that the global strong solution can become classical if the initial data is more regular. Note that the assumptions on the initial density do not exclude that the initial density may vanish in a subset of R3 and that it can be of a non trivially compact support.To our knowledge, this paper contains the first result so far for the global existence of solutions to the full compressible Navier-Stokes equations when density vanishes at infinity (in space). In addition, the exponential decay rate of the strong solution is of independent interest.

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arXiv2014

Incompressible Limit of the Compressible Nematic Liquid Crystal Flow

This paper is concerned with the incompressible limit of the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions in R^N(N = 2, 3). It is rigorously shown that the local (and global) strong solution of the compressible system converges to the local (and global) strong solution of the incompressible system. Furthermore, the convergence rates are also obtained in some sense.

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arXiv2014

Blow-up criterions of strong solutions to 3D compressible Navier-Stokes equations with vacuum

In the paper, we establish a blow-up criterion in terms of the integrability of the density for strong solutions to the Cauchy problem of compressible isentropic Navier-Stokes equations in \mathbb{R}^3 with vacuum, under the assumptions on the coefficients of viscosity: \frac{29μ}{3}>λ. This extends the corresponding results in [20, 36] where a blow-up criterion in terms of the upper bound of the density was obtained under the condition 7μ>λ. As a byproduct, the restriction 7μ>λin [12, 37] is relaxed to \frac{29μ}{3}>λfor the full compressible Navier-Stokes equations by giving a new proof of Lemma 3.1. Besides, we get a blow-up criterion in terms of the upper bound of the density and the temperature for strong solutions to the Cauchy problem of the full compressible Navier-Stokes equations in \mathbb{R}^3. The appearance of vacuum could be allowed. This extends the corresponding results in [37] where a blow-up criterion in terms of the upper bound of (ρ,\frac{1}ρ, θ) was obtained without vacuum. The effective viscous flux plays a very important role in the proofs.

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arXiv2012

Global well-posedness and zero-diffusion limit of classical solutions to the 3D conservation laws arising in chemotaxis

In this paper, we study the relationship between a diffusive model and a non-diffusive model which are both derived from the well-known Keller-Segel model, as a coefficient of diffusion $\varepsilon$ goes to zero. First, we establish the global well-posedness of classical solutions to the Cauchy problem for the diffusive model with smooth initial data which is of small $L^2$ norm, together with some {\it a priori} estimates uniform for $t$ and $\varepsilon$. Then we investigate the zero-diffusion limit, and get the global well-posedness of classical solutions to the Cauchy problem for the non-diffusive model. Finally, we derive the convergence rate of the diffusive model toward the non-diffusive model. It is shown that the convergence rate in $L^\infty$ norm is of the order $O(\varepsilon^{1/2})$. It should be noted that the initial data is small in $L^2$-norm but can be of large oscillations with constant state at far field. As a byproduct, we improve the corresponding result on the well-posedness of the non-difussive model which requires small oscillations.

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arXiv2012

Global spherically symmetric classical solution to compressible Navier-Stokes equations with large initial data and vacuum

In this paper, we obtain a result on the existence and uniqueness of global spherically symmetric classical solutions to the compressible isentropic Navier-Stokes equations with vacuum in a bounded domain or exterior domain Ω of Rn(n >= 2). Here, the initial data could be large. Besides, the regularities of the solutions are better than those obtained in [H.J. Choe and H. Kim, Math. Methods Appl. Sci., 28 (2005), pp. 1-28; Y. Cho and H. Kim, Manuscripta Math., 120 (2006), pp. 91-129; S.J. Ding, H.Y.Wen, and C.J. Zhu, J. Differential Equations, 251 (2011), pp. 1696-1725]. The analysis is based on some new mathematical techniques and some new useful energy estimates. This is an extension of the work of Choe and Kim, Cho and Kim, and Ding, Wen, and Zhu, where the global radially symmetric strong solutions, the local classical solutions in three dimensions, and the global classical solutions in one dimension were obtained, respectively. This paper can be viewed as the first result on the existence of global classical solutions with large initial data and vacuum in higher dimension

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arXiv2012

Global symmetric classical and strong solutions of the full compressible Navier-Stokes equations with vacuum and large initial data

First of all, we get the global existence of classical and strong solutions of the full compressible Navier-Stokes equations in three space dimensions with initial data which is large and spherically or cylindrically symmetric. The appearance of vacuum is allowed. In particular, if the initial data is spherically symmetric, the space dimension can be taken not less than two. The analysis is based on some delicate {\it a priori} estimates globally in time which depend on the assumption $κ=O(1+θ^q)$ where $q>r$ ($r$ can be zero), which relaxes the condition $q\ge2+2r$ in [14,29,42]. This could be viewed as an extensive work of [18] where the equations hold in the sense of distributions in the set where the density is positive with initial data which is large, discontinuous, and spherically or cylindrically symmetric in three space dimension. Finally, with the assumptions that vacuum may appear and that the solutions are not necessarily symmetric, we establish a blow-up criterion in terms of $\|ρ\|_{L^\infty_tL_x^\infty}$ and $\|ρθ\|_{L^4_tL^(12/5)_x}$ for strong solutions.

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