Local well-posedness of the Hall-MHD system in $H^s(\mathbb {R}^n)$ with $s>\frac n2$

Mimi Dai

Local well-posedness of the Hall-MHD system in $H^s(\mathbb {R}^n)$ with $s>\frac n2$

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arxiv 1709.02347 v1 pith:B2CFRBA7 submitted 2017-09-07 math.AP

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classification math.AP

keywords fraclocalmathbbwell-posednesshall-mhdleftrightspace

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abstract

We establish local well-posedness of the Hall-magneto-hydrodynamics (Hall-MHD) system in the Sobolev space $\left(H^s(\mathbb{R}^n)\right)^2$ with $s>\frac n2$. The previously known local well-posedness space was $\left(H^s(\mathbb{R}^n)\right)^2$ with $s>\frac n2+1$. Thus the result presented here is an improvement.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Determining wavenumbers for the incompressible Hall-magneto-hydrodynamics
math.AP 2019-08 conditional novelty 6.0 of 10

Two Hall-MHD solutions that share their low Fourier modes up to a time-dependent determining wavenumber converge to each other in L2 as time goes to infinity.

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