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arXiv · 1010.4755

Convex integration for a class of active scalar equations

Roman Shvydkoy
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Abstract

We show that a general class of active scalar equations, including porous media and certain magnetostrophic turbulence models, admit non-unique weak solutions in the class of bounded functions. The proof is based upon the method of convex integration recently implemented for equations of fluid dynamics in [2,3].

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Roman Shvydkoy. 2010-10-22. Convex integration for a class of active scalar equations. https://arxiv.org/abs/1010.4755

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