Stability and large time decay for the three-dimensional anisotropic magnetohydrodynamic equations

This paper focuses on the stability problem and large time behavior of solutions to the three-dimensional anisotropic magnetohydrodynamic equations. By fully exploiting the structure of the system, the energy methods and the method of bootstrapping argument, we prove the global stability of solutions to this system with initial data small in H-3(R-3). Furthermore, for these global solutions with initial data in H-4(R-3) being large, we obtain its global H-4(R-3) bound which is independent of time. Moreover, the optimal decay rates of these global solutions and its first-order derivatives are established.

Automated summary

This paper focuses on the stability problem and large time behavior of solutions to the three-dimensional anisotropic magnetohydrodynamic equations. By fully exploiting the structure of the system and using energy methods and the method of bootstrapping arguments, the global stability of solutions with small initial data in H-3(R-3) is proven. Furthermore, for global solutions with large initial data in H-4(R-3), a global H-4(R-3) bound which is independent of time is obtained. Moreover, the optimal decay rates of these global solutions and their first-order derivatives are established.