## Communicated by M. Costabel In this work, we improved the regularity criterion on the Cauchy problem for the Navier-Stokes equations in multiplier space in terms of the two partial derivatives of velocity fields, @ 1 u 1 and @ 2 u 2 .
Extension criterion on regularity for weak solutions to the 3D MHD equations
β Scribed by Sadek Gala
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 138 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.1263
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, we consider the regularity criteria for weak solutions to the 3D incompressible magnetohydrodynamic equations and prove some regularity criteria which are related only with u+B or u-B. This is an improvement of the result given by He and Wang (J.
π SIMILAR VOLUMES
## Abstract Consider the nonstationary NavierβStokes equations in Ξ© Γ (0, __T__), where Ξ© is a bounded domain in β^3^. We prove interior regularity for suitable weak solutions under some condition on the pressure in the class of scaling invariance. The notion of suitable weak solutions makes it pos
## Abstract We study the regularity criteria for weak solutions to the incompressible magnetohydrodynamic (MHD) equations. Some regularity criteria, which are related only with __u__+__B__ or __u__β__B__, are obtained for weak solutions to the MHD equations. Copyright Β© 2008 John Wiley & Sons, Ltd.
The propagation of Ho¨lder regularity of the solutions to the 3D Euler equations is discussed. Our method is a special semi-linearization of the vorticity equation combined with the classical Schauder interior estimates.
We extend previous results for the Neumann boundary value problem to the case of boundary data from the space H -1 2 +e (C), 0<e< 1 2 , where C = \*X is the boundary of a two-dimensional cone X with angle b<p. We prove that for these boundary conditions the solution of the Helmholtz equation in X ex