共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
3.
Obtained is the Lp estimate of solutions to the resolvent problem for the Stokes system with interface condition in a bounded domain in . It is the first step to consider the free boundary value problem. 相似文献
4.
Takeshi Taniguchi 《Journal of Differential Equations》2011,251(12):3329-3362
In this paper we consider the existence and uniqueness of weak energy solutions to a stochastic 2-dimensional non-Lipschitz Navier-Stokes equation perturbed by the cylindrical Wiener process W(t) in a bounded or unbounded domain D with the smooth boundary ∂D or D=R2:
5.
Global smooth solutions of the compressible Navier-Stokes equations with density-dependent viscosity
In this paper we study a free boundary problem for the viscous, compressible, heat conducting, one-dimensional real fluids. More precisely, the viscosity is assumed to be a power function of density, i.e., μ(ρ)=ρα, where ρ denotes the density of fluids and α is a positive constant. In addition, the equations of state include and are more general than perfect flows which only depend linearly on temperature. The global existence (uniqueness) of smooth solutions is established with for general, large initial data, which improves the previous results. Moreover, it is also shown that the solutions will not develop vacuum, mass concentration or heat concentration in a finite time provided the initial data are bounded and smooth, and do not contain vacuum. 相似文献
6.
7.
8.
9.
Global well-posedness of incompressible flow in porous media with critical diffusion in Besov spaces
In this paper we study the model of heat transfer in a porous medium with a critical diffusion. We obtain global existence and uniqueness of solutions to the equations of heat transfer of incompressible fluid in Besov spaces with 1?p?∞ by the method of modulus of continuity and Fourier localization technique. 相似文献
10.
11.
12.
13.
14.
Hi Jun Choe 《Journal of Differential Equations》2003,190(2):504-523
We study strong solutions of the isentropic compressible Navier-Stokes equations in a domain . We first prove the local existence of unique strong solutions provided that the initial data ρ0 and u0 satisfy a natural compatibility condition. The important point in this paper is that we allow the initial vacuum: the initial density may vanish in an open subset of Ω. We then prove a new uniqueness result and stability result. Our results are valid for unbounded domains as well as bounded ones. 相似文献
15.
Hyeong-Ohk Bae 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(5):1350-1363
In this paper, we prove some decay properties of global solutions for the Navier-Stokes equations in an exterior domain Ω⊂Rn, n=2,3.When a domain has a boundary, the pressure term is troublesome since we do not have enough information on the pressure near the boundary. To overcome this difficulty, by multiplying a special form of test functions, we obtain an integral equation. He-Xin (2000) [12] first introduced this method and then Bae-Jin (2006, 2007) [1] and [13] modified their method to obtain better decay rates. Also, Bae-Roh (2009) [11] improved Bae-Jin’s results. Unfortunately, their results were not optimal, because there exists an unpleasant positive small δ in their rates.In this paper, we obtain the following optimal rate without δ,
16.
Guilong Gui 《Advances in Mathematics》2010,225(3):1248-1284
In this paper, we consider the stability to the global large solutions of 3-D incompressible Navier-Stokes equations in the anisotropic Sobolev spaces. In particular, we proved that for any , given a global large solution v∈C([0,∞);H0,s0(R3)∩L3(R3)) of (1.1) with and a divergence free vector satisfying for some sufficiently small constant depending on , v, and , (1.1) supplemented with initial data v(0)+w0 has a unique global solution in u∈C([0,∞);H0,s0(R3)) with ∇u∈L2(R+,H0,s0(R3)). Furthermore, uh is close enough to vh in C([0,∞);H0,s(R3)). 相似文献
17.
18.
In this paper, we study the Stokes system in the half-space , with N?2. We give existence and uniqueness results in weighted Sobolev spaces. After the central case of the generalized solutions, we are interested in strong solutions and symmetrically in very weak solutions by means of a duality argument. 相似文献
19.
20.
Songsong Lu 《Journal of Differential Equations》2006,230(1):196-212
First, the existence and structure of uniform attractors in H is proved for nonautonomous 2D Navier-Stokes equations on bounded domain with a new class of distribution forces, termed normal in (see Definition 3.1), which are translation bounded but not translation compact in . Then, the properties of the kernel section are investigated. Last, the fractal dimension is estimated for the kernel sections of the uniform attractors obtained. 相似文献