On global-in-time weak solutions to a 2D full compressible non-resistive MHD system

Abstract

In this paper, we consider a two-dimensional non-resistive magnetohydrodynamic model, taking the fluctuation of absolute temperature into account. Combining the method of weak convergence developed by Lions [20], Feireisl et al. [7, 8] from compressible Navier-Stokes(- Fourier) system and the new technique of variable reduction proposed by Vasseur et al. [26] and refined by Novotny et al. [22] from compressible two-fluid models, weak solutions are shown to exist globally in time with finite energy initial data. The result is the first one on global solvability to full compressible, viscous, non-resistive magnetohydrodynamic system in multi-dimensions with large initial data.

arXiv comment39 pages; all comments are welcome!

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• On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions