Decay properties of solutions to the incompressible magnetohydrodynamics equations in a half space |
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Authors: | Pigong Han Cheng He |
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Affiliation: | 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, , Beijing 100190, China;2. Division of Mathematics, Department of Mathematical and Physical Sciences, National Natural Science Foundation of China, , Beijing, 100085 China |
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Abstract: | We consider the asymptotic behavior of the strong solution to the incompressible magnetohydrodynamics (MHD) equations in a half space. The Lr‐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 Lq ? Lr 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. |
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Keywords: | MHD equations strong solution decay rate half space |
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