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Local mild solutions to three‐dimensional magnetohydrodynamic system in Morrey spaces
Author(s) -
Zeng Zirong
Publication year - 2020
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.7112
Subject(s) - magnetohydrodynamic drive , mathematics , vorticity , compressibility , mathematical analysis , initial value problem , magnetohydrodynamics , energy method , cauchy problem , physics , vortex , plasma , mechanics , quantum mechanics
In this article, we study the Cauchy problem of three‐dimensional (3‐D) incompressible magnetohydrodynamic system with infinite energy initial data. Via some elaborate analysis of the time evolution of both the vorticity ω : = ∇ × u and the current density j = : ∇ × b , the local‐in‐time well‐posedness of mild solutions with arbitrarily large initial data in Morrey spaces is established.