Strong solutions to the incompressible magnetohydrodynamic equations |
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Authors: | Qing Chen Zhong Tan Yanjin Wang |
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Affiliation: | School of Mathematical Sciences, Xiamen University, Fujian 361005, People's Republic of China |
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Abstract: | 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. |
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Keywords: | magnetohydrodynamics strong solutions incompressible vacuum blow‐up |
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