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Strong solutions to the incompressible magnetohydrodynamic equations
Author(s) -
Chen Qing,
Tan Zhong,
Wang Yanjin
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1338
Subject(s) - magnetohydrodynamic drive , mathematics , compressibility , initial value problem , cauchy problem , compatibility (geochemistry) , mathematical analysis , domain (mathematical analysis) , magnetohydrodynamics , energy method , galerkin method , cauchy distribution , mechanics , finite element method , physics , plasma , thermodynamics , geochemistry , quantum mechanics , geology
In this paper, we are concerned with strong solutions to the Cauchy problem for the incompressible Magnetohydrodynamic equations. By the Galerkin method, energy method and the domain expansion technique, we prove the local existence of unique strong solutions for general initial data, develop a blow‐up criterion for local strong solutions and prove the global existence of strong solutions under the smallness assumption of initial data. The initial data are assumed to satisfy a natural compatibility condition and allow vacuum to exist. Copyright © 2010 John Wiley & Sons, Ltd.