From compressible to incompressible, MHD with non-conservative boundary condition

Speaker(s)

Aneta Wróblewska-Kamińska

Affiliation

IMPAN

Language of the talk

English

Date

Nov. 28, 2024, 12:30 p.m.

Room

room 5070

Seminar

Seminar of Mathematical Physics Equations Group

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We consider a general compressible viscous, heat and magnetic conducting fluid described by a compressible Navier–Stokes–Fourier system coupled with induction equation. In particular, we do not assume conservative boundary conditions for temperature and allow heating or cooling on the surface of the domain. 

We are interested in mathematical analysis when Mach, Froude, and Alvén numbers are small - converging to zero. We give a rigorous mathematical justification that in the limit, in case of low stratification, one obtains a modified Oberbeck–Boussinesq–MHD system with nonlocal term or non-local boundary condition for the temperature deviation. Choosing the proper form of background magnetic field, gravitational potential and domain between parallel plates, one also found that the flow is horizontal. The proof is based on analysing weak solutions to the primitive system and relative entropy method. This is a recent joint work with Florian Oschmann and Piotr Gwiazda.

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