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 d...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.展开更多
We prove the global existence of a unique mild solutions to the incompressible MHD equations when the irdtial data are less than the viscosity coefficients in a new critical space introduced by Lei and Lin[1].Moreover...We prove the global existence of a unique mild solutions to the incompressible MHD equations when the irdtial data are less than the viscosity coefficients in a new critical space introduced by Lei and Lin[1].Moreover,we prove that solutions decay to zero as time goes to infinity.展开更多
基金the National Natural Science Foundation of China (No. 11471103)。
文摘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.
文摘We prove the global existence of a unique mild solutions to the incompressible MHD equations when the irdtial data are less than the viscosity coefficients in a new critical space introduced by Lei and Lin[1].Moreover,we prove that solutions decay to zero as time goes to infinity.
