共查询到20条相似文献,搜索用时 15 毫秒
1.
G. A. Seregin 《Journal of Mathematical Sciences》2002,109(5):1984-1996
The initial boundary-value problem for the modified NavierStokes equations is considered in the case of homogeneous Dirichlet boundary conditions. Under some assumptions, partial regularity for its solution is proved. It is shown that Hausdorff's dimension of the set of singular points is not greater than three. Bibliography: 8 titles. 相似文献
2.
Doklady Mathematics - Classes of exact solutions corresponding to vortex and potential flows are presented within the framework of a hydrodynamic model describing flows of a viscous incompressible... 相似文献
3.
Consider axisymmetric strong solutions of the incompressible Navier–Stokes equations in ?3 with non-trivial swirl. Let z denote the axis of symmetry and r measure the distance to the z-axis. Suppose the solution satisfies, for some 0 ≤ ε ≤ 1, |v (x, t)| ≤ C ? r ?1+ε |t|?ε/2 for ? T 0 ≤ t < 0 and 0 < C ? < ∞ allowed to be large. We prove that v is regular at time zero. 相似文献
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Doklady Mathematics - A three-dimensional initial-boundary value problem for the isentropic equations of the dynamics of a viscous gas is considered. The concentration phenomenon is that, for... 相似文献
6.
In the present paper, we prove the existence of global solutions for the Navier–Stokes equations in Rnwhen the initial velocity belongs to the weighted weak Lorentz space Λn,∞(u) with a sufficiently small norm under certain restriction on the weight u. At the same time, self-similar solutions are induced if the initial velocity is, besides, a homogeneous function of degree-1. Also the uniqueness is discussed. 相似文献
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We prove that a weak solution u = (u 1, u 2, u 3) to the Navier–Stokes equations is strong, if any two components of u satisfy Prodi–Ohyama–Serrin's criterion. As a local regularity criterion, we prove u is bounded locally if any two components of the velocity lie in L 6, ∞. 相似文献
9.
Local regularity of axially symmetric solutions to the Navier–Stokes equations is studied. It is shown that under certain natural assumptions there are no singularities of Type I. 相似文献
10.
Zhen-hua Guo 《应用数学学报(英文版)》2005,21(4):637-654
In this paper, we study the large time asymptotic behavior of solutions to both the Cauchy problem and the exterior problem of the Stokes approximation equations of two dimensional compressible flows. 相似文献
11.
《偏微分方程通讯》2013,38(7-8):955-987
Abstract We study boundary regularity of weak solutions of the Navier–Stokes equations in the half-space in dimension n ≥ 3. We prove that a weak solution u which is locally in the class L p, q with 2/p + n/q = 1, q > n near boundary is Hölder continuous up to the boundary. Our main tool is a pointwise estimate for the fundamental solution of the Stokes system, which is of independent interest. 相似文献
12.
We prove, on one hand, that for a convenient body force with values
in the distribution space (H
-1(D))
d
, where D is the geometric
domain of the fluid, there exist a velocity u and a pressure p
solution of the stochastic Navier–Stokes equation in dimension
2, 3 or 4.
On the other hand, we prove that, for a body force with values in the
dual space V of the divergence free subspace V of (H
1
0(D))
d
,
in general it is not possible to solve the stochastic Navier–Stokes
equations.
More precisely, although such body forces have been considered, there
is no topological space in which Navier–Stokes equations could be
meaningful for them. 相似文献
13.
We consider a system of equations of the boundary layer derived from the hydrodynamical system for generalized Newtonian media. This modification of the Navier–Stokes system was proposed by O. A. Ladyzhenskaya in connection with the uniqueness of the solution of this system in general. We prove the existence and the uniqueness of a solution for the problem of continuation of the boundary layer and consider some questions connected with the separation of the boundary layer. 相似文献
14.
We establish a sufficient regularity condition for local solutions of the Navier–Stokes equations. For a suitable weak solution (u, p) on a domain D we prove that if \(\partial _3 u\) belongs to the space \(L_t^{s_0}L_x^{r_0}(D)\) where \(2/s_0 + 3/r_0 \le 2 \) and \(9/4 \le r_0\le 5/2\), then the solution is Hölder continuous in D. 相似文献
15.
In this paper we want to establish sharp rates of both L~2 and L~∞ decay of glo-bal solutions to the initial value problems for 2-dimensional incompressible Navier-Stokes equations, with, initial data U_0(x)∈L_1∩L~2. U_t + U·U -△U + p = 0,·U = 0,U(x,0) = U_0(x), (1)where U = U(x,t) = (U_1(x,t),U_2(x,t)) is a real vector valued function, △is 2-di-mensional Laplace operator, is gradient operator. We will present a simple method for establishing the decay results. 相似文献
16.
《Journal de Mathématiques Pures et Appliquées》2003,82(8):949-973
We prove the existence of global weak solutions to the Navier–Stokes equations for compressible isentropic fluids for any γ>1 when the Cauchy data are axisymmetric, where γ is the specific heat ratio. Moreover, we obtain a new integrability estimate of the density in any neighborhood of the symmetric axis (the singularity axis). 相似文献
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Reinhard Farwig 《偏微分方程通讯》2013,38(11):1579-1606
We consider the Navier–Stokes equations for a compressible, viscous fluid with heat–conduction in a bounded domain of IR2 or IR3. Under the assumption that the external force field and the external heat supply are small we prove the existence and local uniqueness of a stationary solution satisfying a slip boundary condition. For the temperature we assume a Dirichlet or an oblique boundary condition. 相似文献
19.
Considering the simplified Navier–Stokes equations for the motion of a viscous gas under the adherence condition, we define a weak solution and prove an existence theorem by means of a priori estimates. 相似文献
20.
《Chaos, solitons, and fractals》1999,10(8):1309-1320
The (constrained) canonical reduction of four dimensional self-dual Yang–Millstheory to 2, (2+1) dimensional sine-Gordon theory and 2 dimensional Liouvilles theory areconsidered. The Bäcklund transformations (BTs) areimplemented to obtain new classes of exact solutions for the reduced 2 dimensional sine-Gordonand Liouville models. Another transformation is developed and used to obtain exact solution forthe 2+1 and the original 3+1 sine-Gordon models. 相似文献