Global existence of strong solutions to the multi-dimensional inhomogeneous incompressible MHD equations

DOI10.1016/J.AMC.2022.127154arXiv2107.03654MaRDI QIDQ6372289

Baoquan Yuan, Xueli Ke

Publication date: 8 July 2021

Abstract: This paper is concerned with the Cauchy problem of the multi-dimensional incompressible magnetohydrodynamic equations with inhomogeneous density and fractional dissipation. It is shown that when $$ satisfying $$ and $fracn4<alpha$ for $ngeq3$ , then the inhomogeneous incompressible MHD equations has a unique global strong solution for the initial data in Sobolev space which do not need a small condition.

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

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