Global Existence Of Large Solutions To The Compressible Hall-MHD Equations

This paper is concerned with the global existence of large solutions to the initial-boundary value problems of the compressible Hall-MHD equations with temperature-dependent heat conductivity and density-dependent magnetic diffu-sivity.We first reduce the three dimensional Hall-MHD equations to a quasi-one dimensional form for a special flow like pipe flow,and transfer the resulting e-quations under Euler coordinates into the corresponding form under Lagrangians.Then,under the assumptions of the heat ?=??q(q? 0)and the magnetic diffusivity ?=(?)?-q1(q1?0),we obtianconductivity the global existence of strong soutions based on the theorem of local existence and the a priori estimates.It is showed that neither vacuum nor shock waves in the solutions are developed in fi-nite time provided that the initial conditions have neither vacuum nor shock waves.The key point of this peper is to get the lower and upper bounds of temperature and density.