WELL-POSEDNESS AND STABILITY FOR THE GENERALIZED INCOMPRESSIBLE MAGNETO-HYDRODYNAMIC EQUATIONS IN CRITICAL FOURIER-BESOV-MORREY SPACES

doi:10.1007/s10473-019-0607-6

Abstract

Abstract: This paper concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic (GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory, we get local well-posedness results of the GMHD equations with large initial data (u₀, b₀) belonging to the critical Fourier-Besov-Morrey spaces FṄ_p,λ,q^{1-2α+ 3/p'+λ/p} (R³). Moreover, stability of global solutions is also discussed.

Key words: magneto-hydrodynamic, Fourier-Besov-Morrey space, stability

CLC Number:

35Q35

Azzeddine EL BARAKA, Mohamed TOUMLILIN. WELL-POSEDNESS AND STABILITY FOR THE GENERALIZED INCOMPRESSIBLE MAGNETO-HYDRODYNAMIC EQUATIONS IN CRITICAL FOURIER-BESOV-MORREY SPACES[J].Acta mathematica scientia,Series B, 2019, 39(6): 1551-1567.

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