首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 90 毫秒
1.
This paper concerns the Cauchy problem of the two-dimensional full compressible magnetohydrodynamic equations with zero heat-conduction and vacuum as far field density. In particular, the initial density can have compact support. We prove that the Cauchy problem admits a local strong solution provided both the initial density and the initial magnetic field decay not too slow at infinity.  相似文献   

2.
This paper concerns the global existence and the large time behavior of strong and classical solutions to the two-dimensional (2D) Stokes approximation equations for the compressible flows. We consider the unique global strong solution or classical solution to the 2D Stokes approximation equations for the compressible flows together with the space-periodicity boundary condition or the no-stick boundary condition or Cauchy problem for arbitrarily large initial data. First, we prove that the density is bounded from above independent of time in all these cases. Secondly, we show that for the space-periodicity boundary condition or the no-stick boundary condition, if the initial density contains vacuum at least at one point, then the global strong (or classical) solution must blow up as time goes to infinity.  相似文献   

3.
The aim of this paper is to establish the global well-posedness and large-time asymptotic behavior of the strong solution to the Cauchy problem of the two-dimensional compressible Navier–Stokes equations with vacuum. It is proved that if the shear viscosity \({\mu}\) is a positive constant and the bulk viscosity \({\lambda}\) is the power function of the density, that is, \({\lambda=\rho^{\beta}}\) with \({\beta \in [0,1],}\) then the Cauchy problem of the two-dimensional compressible Navier–Stokes equations admits a unique global strong solution provided that the initial data are of small total energy. This result can be regarded as the extension of the well-posedness theory of classical compressible Navier–Stokes equations [such as Huang et al. (Commun Pure Appl Math 65:549–585, 2012) and Li and Xin (http://arxiv.org/abs/1310.1673) respectively]. Furthermore, the large-time behavior of the strong solution to the Cauchy problem of the two-dimensional barotropic compressible Navier–Stokes equations had been also obtained.  相似文献   

4.
A Wentzell–Freidlin type large deviation principle is established for the two-dimensional Navier–Stokes equations perturbed by a multiplicative noise in both bounded and unbounded domains. The large deviation principle is equivalent to the Laplace principle in our function space setting. Hence, the weak convergence approach is employed to obtain the Laplace principle for solutions of stochastic Navier–Stokes equations. The existence and uniqueness of a strong solution to (a) stochastic Navier–Stokes equations with a small multiplicative noise, and (b) Navier–Stokes equations with an additional Lipschitz continuous drift term are proved for unbounded domains which may be of independent interest.  相似文献   

5.
This paper is concerned with the inflow problem for the one-dimensional compressible Navier–Stokes equations. For such a problem, Matsumura and Nishihara showed in [10] that there exists boundary layer solution to the inflow problem, and that both the boundary layer solution, the rarefaction wave, and the superposition of boundary layer solution and rarefaction wave are nonlinear stable under small initial perturbation. The main purpose of this paper is to show that similar stability results for the boundary layer solution and the supersonic rarefaction wave still hold for a class of large initial perturbation which can allow the initial density to have large oscillation. The proofs are given by an elementary energy method and the key point is to deduce the desired lower and upper bounds on the density function.  相似文献   

6.
The paper is devoted to studying controllability properties for 3D Navier–Stokes equations in a bounded domain. We establish a sufficient condition under which the problem in question is exactly controllable in any finite-dimensional projection. Our sufficient condition is verified for any torus in R3R3. The proofs are based on a development of a general approach introduced by Agrachev and Sarychev in the 2D case. As a simple consequence of the result on controllability, we show that the Cauchy problem for the 3D Navier–Stokes system has a unique strong solution for any initial function and a large class of external forces.  相似文献   

7.
We establish a connection between the strong solution to the spatially periodic Navier–Stokes equations and a solution to a system of forward–backward stochastic differential equations (FBSDEs) on the group of volume-preserving diffeomorphisms of a flat torus. We construct representations of the strong solution to the Navier–Stokes equations in terms of diffusion processes.  相似文献   

8.
Even though the system of the compressible Navier–Stokes equations is not a limiting system of the Boltzmann equation when the Knudsen number tends to zero, it is the second order approximation by applying the Chapman–Enskog expansion. The purpose of this paper is to justify this approximation rigorously in mathematics. That is, if the difference between the initial data for the compressible Navier–Stokes equations and the Boltzmann equation is of the second order of the Knudsen number, so is the difference between two solutions for all time. The analysis is based on a refined energy method for a fluid-type system using the techniques for the system of viscous conservation laws.  相似文献   

9.
We consider the Cauchy problem for the Hopf equation corresponding to the two-dimensional Navier–Stokes equations. The global uniqueness of a solution is proved under the condition that the mean energy of the initial measure is finite, without any additional conditions, i.e., under the same assumptions as in the existence theorem. Thereby we receive a sharp improvement of Foias’s result obtained in the 1970’s about the uniqueness of a spatial statistical solution. Bibliography: 12 titles.  相似文献   

10.
We show existence and regularity of solution for the compressible viscous steady state Navier–Stokes system on a polygon having a grazing corner and that the density has a jump discontinuity across a curve inside the domain. There are corresponding jumps in derivatives of the velocity. The solution comes from a well-posed boundary value problem on a polygonal domain with a non-convex corner. A formula for the decay of the jump is given. The decay formula suggests that density jumps can occur in a compressible flow with a non-vanishing viscosity.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号