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Strong solutions to the incompressible magnetohydrodynamic equations

✍ Scribed by Qing Chen; Zhong Tan; Yanjin Wang

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
220 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

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.

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