Asymptotic behavior of the stationary magnetohydrodynamic equations in an exterior domain

Abstract

In this paper, we study the asymptotic behavior of solutions to the incompressible magnetohydrodynamic (MHD) equations in an exterior domain. We will show that, under some assumption, any nontrivial velocity field u and magnetic field h obey a minimal decaying rate exp(−C|x|² log |x|) at infinity. Our proof is based on appropriate Carleman estimates. As a consequence, we establish a Liouville-type result for the three dimensional incompressible MHDs in an exterior domain.