Well-posedness, analyticity and time decay of the 3D fractional magneto-hydrodynamics equations in critical Fourier-Besov-Morrey spaces with variable exponent. (English) Zbl 1500.35221
Summary: In this paper, we establish the global well-posedness and analyticity of the 3D fractional magnetohydrodynamics equations in the critical Fourier-Besov-Morrey spaces with variable exponent, which can be seen as a meaningful complement to the corresponding results of the magnetohydrodynamics equations in usual Fourier-Besov-Morrey spaces. Furthermore, we get time decay rate estimate of mild solutions.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35S30 | Fourier integral operators applied to PDEs |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 42B37 | Harmonic analysis and PDEs |
| 46F30 | Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) |
| 49N60 | Regularity of solutions in optimal control |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
fractional magneto-hydrodynamic (FMHD) equations; global well-posedness; analytic solution; decay estimates; Littlewood-Paley theory; Fourier-Morrey-Besov spaces with variable exponentsReferences:
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