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

Authors：Zhu, Limei; Zi, Ruizhao^*

Source：Journal of Differential Equations, 2021, 288: 1-39.

DOI：10.1016/j.jde.2021.04.010

• Convergence to equilibrium
• Global smooth solutions
• Compressible magnetohydrodynamic equations

Consider the time decay rates of the smooth solution to the compressible MHD system on T-3. It is shown that if the density rho 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.