Azzeddine El Baraka, Mohamed Toumlilin
Abstract:
This article concerns the Cauchy problem of the 3D generalized incompressible
magneto-hydrodynamic (GMHD) equations. By using the Fourier localization
argument and the Littlewood-Paley theory as in [5,31], we
obtain global well-posedness results of the GMHD equations with small initial
data belonging to the critical Fourier-Besov-Morrey spaces.
Moreover, we prove that the corresponding global solution decays to zero
as time approaches infinity.
Submitted December 28, 2016. Published March 4, 2017.
Math Subject Classifications: 35Q30, 76D05, 76D03.
Key Words: Magneto-hydrodynamic equations; global well-posedness;
Fourier-Besov-Morrey space.
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Azzeddine El Baraka University Mohamed Ben Abdellah FST Fes-Saiss, Laboratory AAFA Department of Mathematics, B.P. 2202 Route Immouzer Fes 30000, Morocco email: azzeddine.elbaraka@usmba.ac.ma, az.elbaraka@gmail.com |
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Mohamed Toumlilin University Mohamed Ben Abdellah FST Fes-Saiss, Laboratory AAFA Department of Mathematics, B.P. 2202 Route Immouzer Fes 30000, Morocco email: mohamed.toumlilin@usmba.ac.ma |
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