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Partial regularity of suitable weak solutions to the four‐dimensional incompressible magneto‐hydrodynamic equations
Author(s) -
Han Pigong,
He Cheng
Publication year - 2012
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.2536
Subject(s) - mathematics , compressibility , weak solution , dimension (graph theory) , mathematical analysis , hausdorff dimension , navier–stokes equations , hausdorff distance , set (abstract data type) , solution set , distribution (mathematics) , pure mathematics , physics , computer science , thermodynamics , programming language
In this paper, we study the partial regularity of suitable weak solutions to the incompressible magneto‐hydrodynamic equations in dimension four by borrowing and improving the arguments given by Caffarelli, Kohn, and Nirenberg for incompressible Navier–Stokes equations. The so‐called ε ‐regularity criteria are established for suitable weak solutions. As an application, an estimate on Hausdorff dimension of the possible singular points set for a suitable weak solution is given. Finally, we present further information on distribution of the possible singular points if the given initial data decay sufficiently rapidly or are not too singular at the origin, in some sense. Copyright © 2012 John Wiley & Sons, Ltd.