Some new regularity criterion for MHD three-dimensional flow

Authors

  • Saeed ur Rahman
  • Tasawar Hayat
  • Hamed H. Alsulami

Keywords:

3D MHD fluid, incompressible, porous medium, regularity criterion, weak solution.

Abstract

The aim of the paper is to establish regularity criteria for the weak solution of fluid passing through the porous media in R^{3}. We  show that if  (grad_{h}u,\partial_{3}b_{3}) belongs to L^{2alpha,2gamma} with 2/alpha+3/gamma<=3, 1<=gamma<=infinity, then the weak solution is regular and unique; if  (grad_{h}u, grad_{h}b) belongs to L^{2alpha,2gamma} with 2/alpha+3/gamma}<=3, 1<=gamma<=infinity, then the weak solution is regular and unique; if  (partial_{3}u, grad u_{3}) belongs to L^{2alpha,2gamma} and (u_{3}, b, \partial_{3} b, grad b_{3}) belongsL^{4alpha,4gamma} with 2/alpha+3/gamma}<=3, 1<=gamma<=infinity, then the weak solution is regular and unique. Here we use the notation grad_{h}=(partial_{1}, partial_{2}).

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Published

01-11-2017