Convex integration for a class of active scalar equations
classification
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classequationsactiveconvexintegrationscalaradmitbounded
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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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