Abstract
The aim of the paper is to establish regularity criteria for the weak solution of fluid passing through the porous media in R', We show that if (del(h)u,partial derivative(3)b(3)) is an element of L-2 alpha,L-2 gamma with 2/alpha + 3/gamma <= 3, 1 <= gamma <= infinity. then the weak solution is regular and unique; if (del(h)u,del(h)b) is an element of L-2 alpha,L-2 gamma with 2/alpha + 3/gamma <= 3, 1 <= gamma <= infinity, then the weak solution is regular and unique; if (partial derivative,u,del u(3)) is an element of L-2 alpha,L-2 gamma and (u(3),b,partial derivative,b del b(2)) is an element of L-4 alpha,L-4 gamma with 2/alpha + 3/gamma <= 3, 1 <= gamma <= infinity , then the weak solution is regular and unique. Here we use the notation del(h) = (partial derivative(1),partial derivative(2)).