On Global-in-Time Weak Solutions to a Two-Dimensional Full Compressible NonResistive MHD System
Yang Li, Yongzhong Sun
Abstract
In this paper, we consider a two-dimensional nonresistive magnetohydrodynamic model, taking the fluctuation of absolute temperature into account. Combining the method of weak convergence developed by Lions [Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models, Clarendon Press, Oxford, UK, 1998] and Feireisl et al. [E. Feireisl and A. Novotný, Singular Limits in Thermodynamics of Viscous Fluids, Birkhauser Verlag, Basel, 2009; E. Feireisl, A. Novotný, and H. Petzeltová, J. Math. Fluid Mech., 3 (2001), pp. 358--392] from compressible Navier--Stokes(--Fourier) system and the new technique of variable reduction proposed by Vasseur, Wen, and Yu [J. Math. Pure. Appl., 125 (2019), pp. 247--282] and refined by Novotný and Pokorný [Arch. Ration. Mech. Anal., 235 (2020), pp. 355--403] 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 a full compressible, viscous, nonresistive magnetohydrodynamic system in multidimensions with large initial data.