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Decay estimates of the smooth solution to the compressible magnetohydrodynamic equations on T3

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Abstract Consider the time decay rates of the smooth solution to the compressible MHD system on T 3 . It is shown that if the density ρ is uniformly bounded… Click to show full abstract

Abstract Consider the time decay rates of the smooth solution to the compressible MHD system on T 3 . It is shown that if the density ρ is uniformly bounded from up and below, and the L 6 norm of the magnetic H is uniformly bounded, then all derivatives of the smooth solution to the compressible MHD system decay exponentially fast to the equilibrium. Furthermore, we construct a global smooth solution obeying these decay rates with small energy but possibly large oscillations.

Keywords: decay estimates; smooth solution; equations decay; estimates smooth; solution; solution compressible

Journal Title: Journal of Differential Equations
Year Published: 2021

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