Journal
APPLIED MATHEMATICS LETTERS
Volume 68, Issue -, Pages 117-121Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2017.01.007
Keywords
Global smooth solution; Generalized MHD equations; Large initial data
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Funding
- Scientific Research Funds of Huaqiao University [14BS309]
- Natural Science Foundation of Fujian Province of China [2015J01582]
- NSFC [11526091, 11626116]
- Natural Science Foundation of Zhejiang Province of China [LQ17A010006]
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This paper considers the global regularity to the 3D generalized MHD equations with the fractional dissipation and magnetic diffusion (-Delta)(alpha) for 0 < alpha < 5/4. Let mu, v, u and b denote the viscosity coefficient, magnetic diffusivity, velocity field and magnetic field, respectively. It is shown that parallel to(u, b)parallel to(s)(H) (s > 5/2 alpha) is globally bounded as long as vertical bar mu - nu vertical bar ( mu + nu)(-1) and (H)(5/2 - alpha) over dot -norm on (u(0) - b(0)) or (u(0) + b(0)) sufficiently small, which generalizes the previous result about large solutions in He et al. (2014). (C) 2017 Elsevier Ltd. All rights reserved.
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