MHD equations with regularity in one direction (Q2019129)
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scientific article; zbMATH DE number 6420097
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | MHD equations with regularity in one direction |
scientific article; zbMATH DE number 6420097 |
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MHD equations with regularity in one direction (English)
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27 March 2015
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Summary: We consider the 3D MHD equations and prove that if one directional derivative of the fluid velocity, say, \(\partial_3\mathbf{u}\in L^p(0,T;L^q(\mathbb {R}^3))\), with \(2/p+3/q=\gamma\in [1,3/2)\), \(3/\gamma \leq q\leq 1/(\gamma -1)\), then the solution is in fact smooth. This improves previous results greatly.
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regularity
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magneto-hydrodynamics (MHD) equations
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