Low Mach number limit of the compressible Euler-Cattaneo-Maxwell equations. (English) Zbl 07461634

Summary: We study the low Mach number limit of the compressible Euler-Cattaneo-Maxwell (ECM) equations with small variations of density, temperature and heat flux. For well-prepared initial data, we prove that, in the framework of classical solutions, the solution of the compressible ECM equations converges to that of the incompressible Euler-Maxwell equations as the Mach number tends to zero. We also obtain the convergence rate and establish the local existence of classical solution to the limit equations. Furthermore, we discuss briefly the low Mach limits of the isentropic Euler-Maxwell equations, the non-isentropic Euler-Maxwell equations without heat conduction, the Euler-Maxwell equations with linear Cattaneo’s heat transfer law and the Euler-Fourier-Maxwell equations. We find that they share the same limit equations, i.e., the incompressible Euler-Maxwell equations. This confirms a physical fact that for the well-prepared initial data and considering small variations of density, temperature and heat flux, the various types of non-isentropic Euler-Maxwell equations have the similar incompressibility as the isentropic equations.


76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35L45 Initial value problems for first-order hyperbolic systems
35B40 Asymptotic behavior of solutions to PDEs
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