GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY*

doi:10.1007/s10473-024-0507-2

Abstract

Abstract: We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations, with the initial data $(u_{0},B_{0})$ being located in the critical Besov space $\dot{B}_{p,1}^{-1+\frac{2}{p}}(\mathbb{R}^{2}) \,\, (1<p<2)$ and the initial density $\rho_{0}$ being close to a positive constant. By using weighted global estimates, maximal regularity estimates in the Lorentz space for the Stokes system, and the Lagrangian approach, we show that the 2-D MHD equations have a unique global solution.

Key words: inhomogeneous MHD equations, electrical conductivity, global unique solutions

CLC Number:

35Q35

Xueli KE. GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY^*[J].Acta mathematica scientia,Series B, 2024, 44(5): 1747-1765.

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References

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GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY^*

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