A remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero kinematic viscosity

In this paper,we study the blow-up criterion of smooth solutions to the 3D magneto-hydrodynamic system in ˙ B 0 ∞,∞.We show that a smooth solution of the 3D MHD equations with zero kinematic viscosity in the whole space R 3 breaks down if and only if certain norm of the vorticity blows up at the same time.     

关于二维光滑线性方程无解的注记

Abstract. A smooth linear complex partial differential equation in two variables which is without solutions is found.     

关于解矩阵方程AX=B的注记

本培出了解矩阵方程AX=B的一个注记。     

关于Suzuki群与射影平面的一个注记

设G Aut(D)且Soc(G) =Sz(q) ,这里q=2 p,p为奇素数,若有Sz(q) 相似文献   

关于渐近拟非扩张算子不动点迭代逼近的注记

研究Banach空间中渐近拟非扩张算子及渐近φ-半压缩算子不动点的迭代逼近问题，给出带误差Ishikawa型迭代序列收敛的充要条件，所得结果修正与改进了[1]的主要结果，且推广了[2]及其他一些文献的相关结果。     

奇异半线性反应扩散方程初值问题的一些注记

考虑下述奇异半线性反应扩散方程初值问题(()-1-t△u=ut+f(x),t＞0,x∈RN lim u(t,x)=0,x∈RN t→0=)其中r＞0,△=∑( )/( )x2i,f(x)非负且f(x)∈L∞(RN).首先利用增算子不动点定理,重新证明了IVP在(0,+∞)上至少存在一个非负解,并给出了IVP解的迭代逼近序列.其次获得了一个有关IVP(1)正解的无限增长性的结果.最后,证明了当r＞1时,去掉条件1/r-1≥n/2,IVP的正解u(t)同样会产生爆破.研究结果表明情形limut→+∞(t,x)=+∞不会出现.     

关于Banach空间一阶非线性脉冲积分-微分方程初值问题解存在性的注记

设m(t)∈C[Jk,R ](k=1,2,…,m),且满足不等式m(t)<(L1 L2t)∫tn(s)ds L3t∫a m(s)ds ∑o0满足KaLs(eδ(L1 aL2)-1)相似文献   

关于近Hermitian流形的注记(英文)

We give a necessary and sufficient condition for an almost Hermitian manifold to be a Kahler manifold. By making use of this condition, we give a new proof of Goldberg＇s theorem.     

关于纤维一般拓扑的一点注记(英文)

Some characterizations of paracompact maps are given in this note, and some equivalent statements of collectionwise normal maps are discussed. And also we show that if f ： X→Y is a closed collectionwise normal map, and f^-1（y） is a semistratifiable subspace of X for any y ∈ Y, then f is a paracompact map.