Convex integration for a class of active scalar equations

Details Convex integration for a class of active scalar equations Convex integration for a class of active scalar equations

2010-10-22

arxiv.org/abs/1010.4755v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

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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