共查询到20条相似文献,搜索用时 15 毫秒
1.
Changjiang Zhu 《Communications in Mathematical Physics》2010,293(1):279-299
In this paper, we study the one-dimensional Navier-Stokes equations connecting to vacuum state with a jump in density when
the viscosity depends on the density. Precisely, when the viscosity coefficient μ(ρ) is proportional to ρ
θ
with θ > 0, where ρ is the density, we give the asymptotic behavior and the decay rate of the density function ρ(x, t). Furthermore, the behavior of the density function ρ(x, t) near the interfaces separating the gas from vacuum and the expanding rate of the interfaces are also studied. The analysis
is based on some new mathematical techniques and some new useful estimates. This fills a final gap on studying Navier-Stokes
equations with the viscosity coefficient μ(ρ) dependent on the density ρ. 相似文献
2.
The compactness properties of solutions to time-discretization of compressible Navier-Stokes equations are investigated in three dimensions. The existence of generalized solutions is established. 相似文献
3.
针对有壁面边界的可压缩流动问题,提出与基于非等距网格的高精度紧致型差分格式相结合的简化隐式迭代时间推进法,建立求解可压缩Navier-Stokes方程的直接数值模拟方法,提高了计算效率.应用该方法,直接数值模拟两种有壁面边界的二维可压缩流动问题,即可压缩平板边界层流动和可压缩槽道流动. 相似文献
4.
In this paper, we study the finite time blow up of smooth solutions to the Compressible Navier-Stokes system when the initial data contain vacuums. We prove that any classical solutions of viscous compressible fluids without heat conduction will blow up in finite time, as long as the initial data has an isolated mass group (see Definition 2.2). The results hold regardless of either the size of the initial data or the far fields being vacuum or not. This improves the blowup results of Xin (Comm Pure Appl Math 51:229–240, 1998) by removing the crucial assumptions that the initial density has compact support and the smooth solution has finite total energy. Furthermore, the analysis here also yields that any classical solutions of viscous compressible fluids without heat conduction in bounded domains or periodic domains will blow up in finite time, if the initial data have an isolated mass group satisfying some suitable conditions. 相似文献
5.
6.
In this paper we consider the isentropic compressible magnetohydrodynamic equations in three space dimensions, and establish a blow-up criterion of classical solutions, which depends on the gradient of the velocity and magnetic field. 相似文献
7.
Asymptotic Analysis for a Vlasov-Fokker-Planck/ Compressible Navier-Stokes System of Equations 总被引:1,自引:0,他引:1
This article is devoted to the asymptotic analysis of a system of coupled kinetic and fluid equations, namely the Vlasov-Fokker-Planck
equation and a compressible Navier-Stokes equation. Such a system is used, for example, to model fluid-particle interactions
arising in sprays, aerosols or sedimentation problems. The asymptotic regime corresponding to a strong drag force and a strong
Brownian motion is studied and the convergence toward a two phase macroscopic model is proved. The proof relies on a relative
entropy method.
A. Mellet was partially supported by NSF grant DMS-0456647. 相似文献
8.
The compressible Navier-Stokes system (CNS) with density-dependent viscosity coefficients is considered in multi-dimension,
the prototype of the system is the viscous Saint-Venat model for the motion of shallow water. A spherically symmetric weak
solution to the free boundary value problem for CNS with stress free boundary condition and arbitrarily large data is shown
to exist globally in time with the free boundary separating fluids and vacuum and propagating at finite speed as particle
path, which is continuous away from the symmetry center. Detailed regularity and Lagrangian structure of this solution have
been obtained. In particular, it is shown that the particle path is uniquely defined starting from any non-vacuum region away
from the symmetry center, along which vacuum states shall not form in any finite time and the initial regularities of the
solution is preserved. Starting from any non-vacuum point at a later-on time, a particle path is also uniquely defined backward
in time, which either reaches at some initial non-vacuum point, or stops at a small middle time and connects continuously
with vacuum. In addition, the free boundary is shown to expand outward at an algebraic rate in time, and the fluid density
decays and tends to zero almost everywhere away from the symmetry center as the time grows up. This finally leads to the formation
of vacuum state almost everywhere as the time goes to infinity. 相似文献
9.
We are concerned with spherically symmetric solutions of the Euler equations for multidimensional compressible fluids, which are motivated by many important physical situations. Various evidences indicate that spherically symmetric solutions of the compressible Euler equations may blow up near the origin at a certain time under some circumstance. The central feature is the strengthening of waves as they move radially inward. A longstanding open, fundamental problem is whether concentration could be formed at the origin. In this paper, we develop a method of vanishing viscosity and related estimate techniques for viscosity approximate solutions, and establish the convergence of the approximate solutions to a global finite-energy entropy solution of the isentropic Euler equations with spherical symmetry and large initial data. This indicates that concentration is not formed in the vanishing viscosity limit, even though the density may blow up at a certain time. To achieve this, we first construct global smooth solutions of appropriate initial-boundary value problems for the Euler equations with designed viscosity terms, approximate pressure function, and boundary conditions, and then we establish the strong convergence of the viscosity approximate solutions to a finite-energy entropy solution of the Euler equations. 相似文献
10.
The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional
Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.
Hongjie Dong was partially supported by the National Science Foundation under agreement No. DMS-0111298. Dapeng Du was partially
supported by a postdoctoral grant from School of Mathematical Sciences at Fudan University. 相似文献
11.
In this paper, we consider the compressible Navier–Stokes equations for isentropic flow of finite total mass when the initial
density is either of compact or infinite support. The viscosity coefficient is assumed to be a power function of the density
so that the Cauchy problem is well-posed. New global existence results are established when the density function connects
to the vacuum states continuously. For this, some new a priori estimates are obtained to take care of the degeneracy of the viscosity coefficient at vacuum. We will also give a non-global
existence theorem of regular solutions when the initial data are of compact support in Eulerian coordinates which implies
singularity forms at the interface separating the gas and vacuum.
Received: 28 September 2001 / Accepted: 6 May 2002 Published online: 4 September 2002 相似文献
12.
We consider the vanishing-viscosity limit for the Navier-Stokes equations with certain slip-without-friction boundary conditions in a bounded domain with non-flat boundary. In particular, we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary. The proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity. 相似文献
13.
Daniel Coutand Hans Lindblad Steve Shkoller 《Communications in Mathematical Physics》2010,296(2):559-587
We prove a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(ρ) = C
γ
ρ
γ for γ > 1. The vacuum condition necessitates the vanishing of the pressure, and hence density, on the dynamic boundary, which
creates a degenerate and characteristic hyperbolic free-boundary system to which standard methods of symmetrizable hyperbolic equations cannot be applied. 相似文献
14.
We consider the Euler system for inviscid incompressible fluid flows, and its perturbations in n, n2. We prove global well-posedness of this perturbed Euler system in the Triebel-Lizorkin spaces for initial vorticity which is small in the critical Besov norms. Comparison type theorems about the blow-up of solutions are proved between the Euler system and its perturbations. We also study the possiblity of the self-similar type of blow-up of solutions to the equations. 相似文献
15.
Susan Friedlander Nataša Pavlović Roman Shvydkoy 《Communications in Mathematical Physics》2006,264(2):335-347
It is proved, using a bootstrap argument, that linear instability implies nonlinear instability for the incompressible Navier-Stokes
equations in Lp for all p ∈ (1,∞) and any finite or infinite domain in any dimension n. 相似文献
16.
This is a detailed study on certain dynamics of Navier-Stokes and Euler equations via a combination of analysis and numerics.
We focus upon two main aspects: (a) zero viscosity limit of the spectra of linear Navier-Stokes operator, (b) heteroclinics
conjecture for Euler equation, its numerical verification, Melnikov integral, and simulation and control of chaos. Due to
the difficulty of the problem for the full Navier-Stokes and Euler equations, we also propose and study two simpler models
of them. 相似文献
17.
《Journal of Nonlinear Mathematical Physics》2013,20(3-4):301-311
Abstract Lie reduction of the Navier-Stokes equations to systems of partial differential equations in three and two independent variables and to ordinary differential equations is described. 相似文献
18.
We study an initial boundary value problem for the equations of plane magnetohydrodynamic compressible flows, and prove that
as the shear viscosity goes to zero, global weak solutions converge to a solution of the original equations with zero shear
viscosity. As a by-product, this paper improves the related results obtained by Frid and Shelukhin for the case when the magnetic
effect is neglected.
Supported by NSFC (Grant No. 10301014, 10225105) and the National Basic Research Program (Grant No. 2005CB321700) of China. 相似文献
19.
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The fluids are acted on by gravity in the bulk, and at the free interfaces we consider both the case of surface tension and the case of no surface forces. We establish a sharp nonlinear global-in-time stability criterion and give the explicit decay rates to the equilibrium. When the upper fluid is heavier than the lower fluid along the equilibrium interface, we characterize the set of surface tension values in which the equilibrium is nonlinearly stable. Remarkably, this set is non-empty, i.e., sufficiently large surface tension can prevent the onset of the Rayleigh-Taylor instability. When the lower fluid is heavier than the upper fluid, we show that the equilibrium is stable for all non-negative surface tensions and we establish the zero surface tension limit. 相似文献
20.
We study regularity criteria for the d-dimensional incompressible Navier-Stokes equations. We prove in this paper that if \({u \in L_\infty^tL_{d}^x((0,T)\times \mathbb{R}^d)}\) is a Leray-Hopf weak solution, then u is smooth and unique in \({(0, T)\times \mathbb{R}^d}\) . This generalizes a result by Escauriaza, Seregin and ?verák [5]. Additionally, we show that if T = ∞ then u goes to zero as t goes to infinity. 相似文献