The Global Well-posedness of Strong Solutions to 2D MHD Equations in Lei-Lin Space
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES(2023)
Abstract
In this paper, we study the Cauchy problem of the 2D incompressible magnetohydrodynamic equations in Lei-Lin space. The global well-posedness of a strong solution in the Lei-Lin space χ −1 (ℝ 2 ) with any initial data in χ −1 (ℝ 2 ) ∩ L 2 (ℝ 2 ) is established. Furthermore, the uniqueness of the strong solution in χ −1 (ℝ 2 ) and the Leray-Hopf weak solution in L 2 (ℝ 2 ) is proved.
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Key words
2d mhd equations,strong solutions,well-posedness,lei-lin
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