Convex integration for a class of active scalar equations

Roman Shvydkoy

Convex integration for a class of active scalar equations

Analysis of PDEs 2010-10-25 v1 Mathematical Physics math.MP

Authors: Roman Shvydkoy

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].

Keywords

weak solutions convex analysis fluid dynamics

Cite

@article{arxiv.1010.4755,
  title  = {Convex integration for a class of active scalar equations},
  author = {Roman Shvydkoy},
  journal= {arXiv preprint arXiv:1010.4755},
  year   = {2010}
}

Comments

19 pages

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