# American Institute of Mathematical Sciences

January  2014, 34(1): 121-143. doi: 10.3934/dcds.2014.34.121

## Dissipative solutions and the incompressible inviscid limits of the compressible magnetohydrodynamic system in unbounded domains

 1 Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1 2 IMATH, EA 2134, Université du Sud Toulon-Var, BP 132, 83957 La Garde, France 3 Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, China

Received  August 2012 Published  June 2013

We consider the compressible Navier-Stokes system coupled with the Maxwell equations governing the time evolution of the magnetic field. We introduce a relative entropy functional along with the related concept of dissipative solution. As an application of the theory, we show that for small values of the Mach number and large Reynolds number, the global in time weak (dissipative) solutions converge to the ideal MHD system describing the motion of an incompressible, inviscid, and electrically conducting fluid. The proof is based on frequency localized Strichartz estimates for the Neumann Laplacean on unbounded domains.
Citation: Eduard Feireisl, Antonin Novotny, Yongzhong Sun. Dissipative solutions and the incompressible inviscid limits of the compressible magnetohydrodynamic system in unbounded domains. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 121-143. doi: 10.3934/dcds.2014.34.121
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