Incompressible inviscid limit for the full magnetohydrodynamic flows on expanding domains. (English) Zbl 07250672

Kwon, Young-Sam

Appl. Math., Praha 65, No. 4, 483-509 (2020).

Summary: In this paper we study the incompressible inviscid limit of the full magnetohydrodynamic flows on expanding domains with general initial data. By applying the relative energy method and carrying out detailed analysis on the oscillation part of the velocity, we prove rigorously that the gradient part of the weak solutions of the full magnetohydrodynamic flows converges to the strong solution of the incompressible Euler system in the whole space, as the Mach number, viscosity as well as the heat conductivity go to zero and the domains expand to the whole space. Furthermore, we obtain the convergence rate.

MSC:

35Q30	Navier-Stokes equations
35E15	Initial value problems for PDEs and systems of PDEs with constant coefficients

Keywords:

full magnetohydrodynamic flows; inviscid limit; expanding domain; incompressible limit

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