This article proves the logarithmically improved Serrin＇s criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvem...This article proves the logarithmically improved Serrin＇s criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] （Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365： 806-808） and [18] （Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375：799 802）.展开更多
This paper is concerned with the cauchy problem for the hyperelastic rots equation in Besov space. By virtue of the Littlewood-Paley decomposition, the local well-posedness for the equation in Besov space is establish...This paper is concerned with the cauchy problem for the hyperelastic rots equation in Besov space. By virtue of the Littlewood-Paley decomposition, the local well-posedness for the equation in Besov space is established. Furthermore, the blow-up criterion for the solutions of the hyperelastic rots equation is derived.展开更多
文摘This article proves the logarithmically improved Serrin＇s criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] （Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365： 806-808） and [18] （Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375：799 802）.
基金Supported by the National Natural Science Foundation of China(Grant No.11001107)
文摘This paper is concerned with the cauchy problem for the hyperelastic rots equation in Besov space. By virtue of the Littlewood-Paley decomposition, the local well-posedness for the equation in Besov space is established. Furthermore, the blow-up criterion for the solutions of the hyperelastic rots equation is derived.
