Local Well-Posedness for the Magnetohydrodynamics in the Different Two Liquids Case

Elena Frolova and Yoshihiro Shibata ()
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Elena Frolova: St. Petersburg State Electrotechnical University «LETI», Prof. Popova 5, 191126 St. Petersburg, Russia
Yoshihiro Shibata: Department of Mathematics, Waseda University, Tokyo 169-8555, Japan

Mathematics, 2022, vol. 10, issue 24, 1-45

Abstract: We consider the free boundary problem of MHD in the multi-dimensional case. This problem describes the motion of two incompressible fluids separated by a closed interface under the action of a magnetic field. This problem is overdetermined, and we find an equivalent system of equations which is uniquely solvable locally in time in the L p - L q maximal regularity class, where 1 < p , q < ∞ and 2 / p + N / q < 1 . As a result, the original two-phase problem for the MHD is solvable locally in time.

Keywords: two-phase problem; magnetohydorodynamics; local well-posedness; L p - L q maximal regularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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