Weak solutions to the full MHD system with non-homogeneous boundary conditions

ABSTRACT

This paper is devoted to the study of weak solutions for full compressible magnetohydrodynamic flows in a 3D bounded domain, with non-homogeneous boundary condition for the velocity, absolute temperature and density on the inflow part, with Navier-type slip boundary condition for magnetic field. We show the weak–strong uniqueness principle as well as the global existence under a new notion of weak solution.

KEYWORDS:

• Full magnetohydrodynamic flows
• non-homogeneous boundary conditions
• weak solution
• weak–strong uniqueness principle

MATHEMATICS SUBJECT CLASSIFICATIONS (2010):

• 76W05
• 35D30
• 76N10

Disclosure statement

No potential conflict of interest was reported by the author(s).