Compressible magnetohydrodynamics as a dissipative system
Analysis of PDEs
2023-03-14 v1
Abstract
We consider the complete system of equations governing the motion of a general compressible, viscous, electrically and heat conductive fluid driven by non-conservative boundary conditions. We show the existence of a bounded absorbing set in the energy space and asymptotic compactness of trajectories. As a corollary, the set of all entire globally bounded solutions is identified as a natural attractor. Examples of boundary conditions giving rise to unbounded solutions are also discussed.
Cite
@article{arxiv.2303.06886,
title = {Compressible magnetohydrodynamics as a dissipative system},
author = {Jan Brezina and Eduard Feireisl},
journal= {arXiv preprint arXiv:2303.06886},
year = {2023}
}