共查询到20条相似文献,搜索用时 0 毫秒
1.
Xiangsheng Xu 《Transactions of the American Mathematical Society》1997,349(5):1973-1992
We consider the system , in coupled with suitable initial-boundary conditions, where is a bounded domain in with smooth boundary and is a continuous and positive function of . Our main result is that under some conditions on there exists a relatively open subset of such that is locally Hölder continuous on , the interior of is empty, and is essentially bounded on .
2.
In this paper, we are concerned with the partial regularity for suitable weak solutions of the tri-dimensional magnetohydrodynamic equations. With the help of the De Giorgi iteration method, we obtain the results proved by He and Xin (C. He, Z. Xin, Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations, J. Funct. Anal. 227 (2005) 113–152), namely, the one dimensional parabolic Hausdorff measure of the possible singular points of the velocity field and the magnetic field is zero. 相似文献
3.
In this paper, we study the local behavior of the solutions to the three-dimensional magnetohydrodynamic equations. we are interested in both the uniform gradient estimates for smooth solutions and regularity of weak solutions. It is shown that, in some neighborhood of (x0,t0), the gradients of the velocity field u and the magnetic field B are locally uniformly bounded in L∞ norm as long as that either the scaled local L2-norm of the gradient or the scaled local total energy of the velocity field is small, and the scaled local total energy of the magnetic field is uniformly bounded. These estimates indicate that the velocity field plays a more dominant role than that of the magnetic field in the regularity theory. As an immediately corollary we can derive an estimates of Hausdorff dimension on the possible singular set of a suitable weak solution as in the case of pure fluid. Various partial regularity results are obtained as consequences of our blow-up estimates. 相似文献
4.
5.
In this paper, we establish Hölder regularity of weak solutions to the diagonal divergence form degenerate quasilinear parabolic system related to Hörmander type vector fields by deriving a parabolic Poincaré inequality and the higher integrability of gradients of weak solutions. 相似文献
6.
7.
In this paper we deal with the study of regularity properties of weak solutions to nonlinear, second-order parabolic systems of the type
8.
G. Gripenberg 《Journal of Mathematical Analysis and Applications》2009,352(1):175-183
Sufficient conditions are given for the solutions to the (fully nonlinear, degenerate) elliptic equation F(x,u,Du,D2u)=0 in Ω to satisfy |u(x)−u(y)|?Cα|x−y| for some α∈(0,1) when x∈Ω and y∈∂Ω. 相似文献
9.
10.
Frank Duzaar Giuseppe Mingione 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2005,22(6):705-751
We present a new, complete approach to the partial regularity of solutions to non-linear, second order parabolic systems of the form
ut−divA(x,t,u,Du)=0.