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Decay properties of solutions to the incompressible magnetohydrodynamics equations in a half space
Author(s) -
Han Pigong,
He Cheng
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2538
Subject(s) - magnetohydrodynamics , mathematics , compressibility , space (punctuation) , mathematical analysis , nonlinear system , variable (mathematics) , semigroup , physics , mechanics , magnetic field , quantum mechanics , linguistics , philosophy
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 L 1 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.