Global wellposedness and large time behavior of solutions to the Hall-magnetohydrodynamics equations (Q2658496)

Summary: We prove the global solutions to the incompressible Hall-magnetohydrodynamics (Hall-MHD) equations with small or some large initial data in \(\mathbb R^n (n \geq 3)\). Especially, Fujita-Kato type initial data as the incompressible Navier-Stokes equations are allowed. We also study the large time behavior of the solutions and obtain an optimal decay rate in the general Besov spaces. Different from all the previous wellposedness results in [\textit{D. Chae} and \textit{J. Lee}, J. Differ. Equations 256, No. 11, 3835--3858 (2014; Zbl 1295.35122); \textit{D. Chae} and \textit{M. Schonbek}, J. Differ. Equations 255, No. 11, 3971--3982 (2013; Zbl 1291.35212); \textit{R. Wan} and \textit{Y. Zhou}, J. Differ. Equations 259, No. 11, 5982--6008 (2015; Zbl 1328.35185)], the initial energy we considered here may not be fi nite.