Decay properties of solutions to the incompressible magnetohydrodynamics equations in a half space.

We consider the asymptotic behavior of the strong solution to the incompressible magnetohydrodynamics (MHD) equations in a half space. The L r-decay rates of the strong solution and its derivatives with respect to space variables and time variable, including the L1 and L ∞ decay rates of its first order derivatives with respect to space variables, are derived by using L q − L r estimates of the Stokes semigroup and employing a decomposition for the nonlinear terms in MHD equations. In addition, if the given initial data lie in a suitable weighted space, we obtain more rapid decay rates than observed in general. Similar results are known for incompressible Navier-Stokes equations in a half space under same assumption. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]