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Global wellposedness for Hall-MHD equations. (English) Zbl 1482.76145

Summary: This paper concerns the wellposedness problem of Hall-MHD system. The mild solution of Hall-MHD equations exists globally in the nonhomogeneous Lei-Lin space setting provided that the initial data satisfies \(\| u_0 \|_{\mathcal{X}^{- 1} \cap \mathcal{X}^0} + \| B_0 \|_{\mathcal{X}^{- 1} \cap \mathcal{X}^0} < \min \{\frac{\mu}{2}, \frac{\nu}{4}\}\), where \(\mu\) is the viscosity of the fluid and \(\nu\) is the magnetic diffusion coefficient. Our global existence result covers rougher initial data and improves the previous results.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35Q35 PDEs in connection with fluid mechanics
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