GLOBAL STRONG SOLUTIONS OF THE DENSITY-DEPENDENT INCOMPRESSIBLE MHD SYSTEM WITH ZERO RESISTIVITY IN A BOUNDED DOMAIN | Zendy

Jishan Fan | Zendy; Bessem Samet | Zendy; Yong Zhou | Zendy

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GLOBAL STRONG SOLUTIONS OF THE DENSITY-DEPENDENT INCOMPRESSIBLE MHD SYSTEM WITH ZERO RESISTIVITY IN A BOUNDED DOMAIN

Author(s) -

Jishan Fan,

Bessem Samet,

Yong Zhou

Publication year - 2019

Publication title -

mathematical modelling and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.491

H-Index - 25

eISSN - 1648-3510

pISSN - 1392-6292

DOI - 10.3846/mma.2019.007

Subject(s) - bounded function , zero (linguistics) , magnetohydrodynamics , compressibility , electrical resistivity and conductivity , domain (mathematical analysis) , mathematics , mathematical analysis , physics , magnetic field , mechanics , quantum mechanics , philosophy , linguistics

In this paper, we first establish a regularity criterion for the strong solutions to the density-dependent incompressible MHD system with zero resistivity in a bounded domain. Then we use it and the bootstrap argument to prove the global well-posedness provided that the initial data u0 and b0 satisfy that (d-2)||∇u0 || L2+||b0||w1,p are sufficiently small with . We do not assume the positivity of initial density, it may vanish in an open subset (vacuum) of Ω.

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