Global well-posedness of compressible bipolar Navier-Stokes-Poisson equations

We consider the initial value problem for multi-dimensional bipolar compressible Navier-Stokes-Poisson equations, and show the global existence and uniqueness of the strong solution in hybrid Besov spaces with the initial data close to an equilibrium state.     

Large time behavior of solutions to 3D compressible Navier-Stokes-Poisson system

We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation.If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity,we show that the density converges to its equilibrium state at the L 2-rate (1+t)(-7/4) or L ∞-rate (1+t)(-5/2),and the momentum decays at the L 2-rate (1+t)(-5/4) or L ∞-rate (1+t)(-2).These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.     

Global existence for compressible Navier-Stokes-Poisson equations in three and higher dimensions

The compressible Navier-Stokes-Poisson system is concerned in the present paper, and the global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces in three and higher dimensions.     

Regularity and asymptotic behavior of 1D compressible Navier-Stokes-Poisson equations with free boundary

In this paper, firstly, we consider the regularity of solutions in to the 1D Navier-Stokes-Poisson equations with density-dependent viscosity and the initial density that is connected to vacuum with discontinuities, and the viscosity coefficient is proportional to ρθ with 0<θ<1. Furthermore, we get the asymptotic behavior of the solutions when the viscosity coefficient is a constant. This is a continuation of [S.J. Ding, H.Y. Wen, L. Yao, C.J. Zhu, Global solutions to one-dimensional compressible Navier-Stokes-Poisson equations with density-dependent viscosity, J. Math. Phys. 50 (2009) 023101], where the existence and uniqueness of global weak solutions in H¹([0,1]) for both cases: μ(ρ)=ρθ, 0<θ<1 and μ=constant have been established.     

Global existence of the radially symmetric strong solution to Navier-Stokes-Poisson equations for isentropic compressible fluids

We prove the two existence results of the radially symmetric strong solutions to the Navier- Stokes-Poisson equations for isentropic compressible fluids. The important point in this paper is that the initial density is vacuum. It is different from weak solutions. Now we need some compatibility condition.     

Existence of weak solutions to the three-dimensional steady compressible magnetohydrodynamic equations

The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ 1.The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density,and the method of weak convergence.According to the author's knowledge,it is the first result that treats in three dimensions the existence of weak solutions to the steady compressible MHD equations with γ 1.     

Stability of the planar rarefaction wave to two-dimensional Navier-Stokes-Korteweg equations of compressible fluids

This study is concerned with the large time behavior of the two-dimensional compressible Navier-Stokes-Korteweg equations, which are used to model compressible fluids with internal capillarity. Based on the fact that the rarefaction wave, one of the basic wave patterns to the hyperbolic conservation laws is nonlinearly stable to the one-dimensional compressible Navier-Stokes-Korteweg equations, the planar rarefaction wave to the two-dimensional compressible Navier-Stokes-Korteweg equations is first derived. Then, it is shown that the planar rarefaction wave is asymptotically stable in the case that the initial data are suitably small perturbations of the planar rarefaction wave. The proof is based on the delicate energy method. This is the first stability result of the planar rarefaction wave to the multi-dimensional viscous fluids with internal capillarity.     

Self-similar solutions to the isothermal compressible Navier-Stokes equations

^** Email: guo_zhenhua{at}iapcm.ac.cn^*** Email: jiang{at}iapcm.ac.cn We investigate the self-similar solutions to the isothermalcompressible Navier–Stokes equations. The aim of thispaper is to show that there exist neither forward nor backwardself-similar solutions with finite total energy. This generalizesthe results for the incompressible case in Neas, J., Rika, M.& verák, V. (1996, On Leray's self-similar solutionsof the Navier-Stokes equations. Acta. Math., 176, 283–294),and is consistent with the (unproved) existence of regular solutionsglobally in time for the compressible Navier–Stokes equations.     

Existence of finite energy weak solutions for the equations MHD of compressible fluids

This article concerns the existence of global weak solutions for a compressible Magnetohydrodynamic model. We assume the viscosity and the resistivity to be constant and we prove that Feireisl and Lions's strategies dedicated to the usual barotropic compressible flows may be extended to our system. The only difficulty to be taken into account is the magnetic field dependency. The case with density-dependent viscosity and resistivity coefficients will be treated in a forthcoming paper following Bresch and Desjardins's strategy.     

Large time behaviors of the isentropic bipolar compressible Navier-Stokes-Poisson system

The isentropic bipolar compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l(R3) ∩ B˙ s 1,1 (R3) with l ≥ 4 and s ∈ (0, 1], it is shown that the momenta of the charged particles decay at the optimal rate (1+t) 1 4 s 2 in L2 -norm, which is slower than the rate (1+t) 3 4 s 2 for the compressible Navier-Stokes (NS) equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both (1 + t) 3 4 due to the cancellation effect from the interplay interaction of the charged particles.     

Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system

We prove a stability result of constant equilibria for the three dimensional Navier-Stokes-Poisson system uniform in the inviscid limit. We allow the initial density to be close to a constant and the potential part of the initial velocity to be small independently of the rescaled viscosity parameter ε while the incompressible part of the initial velocity is assumed to be small compared to ε. We then get a unique global smooth solution. We also prove a uniform in ε time decay rate for these solutions. Our approach allows to combine the parabolic energy estimates that are efficient for the viscous equation at ε fixed and the dispersive techniques (dispersive estimates and normal forms) that are useful for the inviscid irrotational system.     

Blow-up criterion for compressible MHD equations

In this paper, we study the 3D compressible magnetohydrodynamic equations. We obtain a blow up criterion for the local strong solutions just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion (see J.T. Beal, T. Kato and A. Majda (1984) [1]) for the ideal incompressible flow. In addition, initial vacuum is allowed in our case.     

Global existence for the non-isentropic compressible Navier-Stokes-Poisson system in three and higher dimensions

We are concerned with the global existence and uniqueness of strong solutions for the non-isentropic compressible Navier-Stokes-Poisson system in the framework of hybrid Besov spaces in three and higher dimensions. These results extend paper (Hao and Li, 2009 [4]) devoted to the barotropic case.     

Asymptotic behaviour of solutions to the Navier-Stokes equations of a two-dimensional compressible flow

In this paper,we are concerned with the asymptotic behaviour of a weak solution to the Navier-Stokes equations for compressible barotropic flow in two space dimensions with the pressure function satisfying p(e) = a log d(e) for large .Here d > 2,a > 0.We introduce useful tools from the theory of Orlicz spaces and construct a suitable function which approximates the density for time going to infinity.Using properties of this function,we can prove the strong convergence of the density to its limit state.The behaviour of the velocity field and kinetic energy is also briefly discussed.     

Stability of weak solutions to the compressible Navier–Stokes equations in bounded annular domains

We prove the Lipschitz continuous dependence on initial data of global spherically symmetric weak solutions to the Navier–Stokes equations of a viscous polytropic ideal gas in bounded annular domains with the initial data in the Lebesgue spaces. Copyright © 2007 John Wiley & Sons, Ltd.     

Global existence of strong solutions of the Navier-Stokes equations for isentropic compressible fluids with density-dependent viscosity

This paper is concerned with global strong solutions of the isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient in one-dimensional bounded intervals. Precisely, the viscosity coefficient μ=μ(ρ) and the pressure P is proportional to ργ with γ>1. The important point in this paper is that the initial density may vanish in an open subset. We also show that the strong solution obtained above is unique provided that the initial data satisfies additional regularity and a compatible condition. Compared with former results obtained by Hyunseok Kim in [H. Kim, Global existence of strong solutions of the Navier-Stokes equations for one-dimensional isentropic compressible fluids, available at: http://com2mac.postech.ac.kr/papers/2001/01-38.pdf], we deal with density-dependent viscosity coefficient.     

Blow-up for 3-D compressible isentropic Navier-Stokes-Poisson equations

Czechoslovak Mathematical Journal - We study compressible isentropic Navier-Stokes-Poisson equations in ?3. With some appropriate assumptions on the density, velocity and potential, we show...     

Global Existence of Strong Solutions of Navier-Stokes-Poisson Equations for One-Dimensional Isentropic Compressible Fluids

The authors prove two global existence results of strong solutions of the isentropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded.