Compressible magnetohydrodynamics as a dissipative system

Jan Brezina; Eduard Feireisl

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arXiv · 2303.06886

Compressible magnetohydrodynamics as a dissipative system

Jan Brezina·Eduard Feireisl

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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.

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Jan Brezina, Eduard Feireisl. 2023-03-13. Compressible magnetohydrodynamics as a dissipative system. https://arxiv.org/abs/2303.06886

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