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Local well‐posedness of the Hall‐MHD system in H s ( R n ) with s > n 2
Author(s) -
Dai Mimi
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800107
Subject(s) - magnetohydrodynamics , sobolev space , hall effect , space (punctuation) , mathematics , zero (linguistics) , mathematical analysis , physics , magnetic field , quantum mechanics , computer science , linguistics , philosophy , operating system
We establish local well‐posedness of the Hall‐magneto‐hydrodynamics (Hall‐MHD) system in the Sobolev space( H s ( R n ) ) 2 with s > n 2 , n ≥ 2 . The previously known local well‐posedness Sobolev space was( H s ( R n ) ) 2 with s > n 2 + 1 . Thus the result presented here is an improvement. Moreover, we show that the solution of the Hall‐MHD system in the space( H s ( R n ) ) 2 with s > n 2converges to a solution of the MHD system when the Hall effect coefficient goes to zero.