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

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  • 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.
    Mathematics Subject Classification: Primary: 35Q30, 35Q60; Secondary: 35B25.

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