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Well-posedness for Hall-magnetohydrodynamics. (English) Zbl 1297.35064
Summary: We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resistive, viscous or inviscid Hall-MHD model. We also show a Liouville theorem for the stationary solutions.

MSC:
35B53 Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs
35L60 First-order nonlinear hyperbolic equations
35K55 Nonlinear parabolic equations
35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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