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Stability of rarefaction wave for the compressible non-isentropic Navier-Stokes-Maxwell equations. (English) Zbl 1471.35225

Summary: We study the large-time asymptotic behavior of solutions toward the rarefaction wave of the compressible non-isentropic Navier-Stokes equations coupling with Maxwell equations under some small perturbations of initial data and also under the assumption that the dielectric constant is bounded. For that, the dissipative structure of this hyperbolic-parabolic system is studied to include the effect of the electromagnetic field into the viscous fluid and turns out to be more complicated than that in the simpler compressible Navier-Stokes system. The proof of the main result is based on the elementary \(L^2\) energy methods.

MSC:

35Q30 Navier-Stokes equations
76N06 Compressible Navier-Stokes equations
76N30 Waves in compressible fluids
76L05 Shock waves and blast waves in fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs
78A25 Electromagnetic theory (general)
35Q61 Maxwell equations
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