Speaker
Description
We consider a general compressible viscous, heat and magnetic conducting fluid described bycompressible Naiver–Stokes–Fourier system coupled with induction equation. In particular we do not assume conservative boundary condition for temperature and allow heating or cooling on the surface of the domain. We are interested in mathematical analysis when Mach, Froude, and Alfvén number are small - converging to zero. We give a rigorous mathematical justification that in the limit, in case of low stratification, one obtains modified Oberbeck–Boussinesq–MHD system with nonlocal term or non-local boundary condition for the temperature deviation. Choosing proper form of background magnetic field, gravitational potential and domain between parallel plates one found also that the flow is horizontal. The proof is based on the analysis of weak solutions to primitive system and relative entropy method. This is a recent joint work with Florian Oschmann and Piotr Gwiazda.
