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上海市数学会青年学者论坛
——偏微分方程论坛

Global Well-posedness and Exponential Decay Rates of the Strong Solutions to the 2D Full Compressible MHD Equations

Speaker

尚朝阳 , 上海立信会计金融学院

Time

19 Dec, 10:40 - 11:20

Abstract

In this talk, we introduce the initial-boundary value problem for the two-dimensional viscous, compressible, and heat conducting magnetohydrodynamics equations with vacuum. When all the coefficients of viscosity, heat conductivity and magnetic diffusivity are constants, first, we show that for general initial data and any time T>0, the local strong solution in the sense of Sobolev norms will never blow-up provided that the density is bounded from above and the temperature belongs to some Sobolev spaces. Second, based on the above blow-up criterion and the delicate analysis of the nonlinear strong coupling equations, we establish the global existence of strong solutions when the initial mass of the fluid and the initial energy of the magnetic field are suitable small, where the refined Zlotnik inequality and the decoupling of the full compressible MHD equations play an essential role in proving the uniform upper bound of the density and the higher-order a priori uniform in time estimates, respectively. It is worth mentioning that the initial velocity and temperature can be large. Moreover, in contrast to the classical theory of the polynomial decay rates for the full compressible MHD equations, we obtain exponential decay rates of the global strong solutions. This is a joint work with Prof. Yachun Li.