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Local well‐posedness of the Hall‐MHD system in Hs(Rn) with s>n2

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  • Mimi Dai

Abstract

We establish local well‐posedness of the Hall‐magneto‐hydrodynamics (Hall‐MHD) system in the Sobolev space (Hs(Rn))2 with s>n2, n≥2. The previously known local well‐posedness Sobolev space was (Hs(Rn))2 with s>n2+1. Thus the result presented here is an improvement. Moreover, we show that the solution of the Hall‐MHD system in the space (Hs(Rn))2 with s>n2 converges to a solution of the MHD system when the Hall effect coefficient goes to zero.

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  • Mimi Dai, 2020. "Local well‐posedness of the Hall‐MHD system in Hs(Rn) with s>n2," Mathematische Nachrichten, Wiley Blackwell, vol. 293(1), pages 67-78, January.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:1:p:67-78
    DOI: 10.1002/mana.201800107
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