## 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 .
The regularity criterion of the weak solution to the 3D viscous Boussinesq equations in Besov spaces
β Scribed by Zhaoyin Xiang
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 209 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.1367
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π SIMILAR VOLUMES
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.
## Abstract We prove the uniqueness of weak solutions of the 3βD timeβdependent GinzburgβLandau equations for superβconductivity with initial data (__Ο__~0~, __A__~0~)β __L__^2^ under the hypothesis that (__Ο__, __A__) β __L__^__s__^(0, __T__; __L__^__r__,β^) Γ$ L^{\bar s} $(0, __T__;$ L^{\bar r,
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