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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Convex integration for a class of active scalar equations
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by R. Shvydkoy PDF
J. Amer. Math. Soc. 24 (2011), 1159-1174 Request permission


We show that a general class of active scalar equations, including porous media and certain magnetostrophic turbulence models, admits 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.
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Additional Information
  • R. Shvydkoy
  • Affiliation: Department of Mathematics, Statistics and Computer Science, 851 S. Morgan St., M/C 249, University of Illinois, Chicago, Illinois 60607
  • Email:
  • Received by editor(s): October 25, 2010
  • Published electronically: June 6, 2011
  • Additional Notes: The work was partially supported by NSF grant DMS – 0907812
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 24 (2011), 1159-1174
  • MSC (2010): Primary 35Q35; Secondary 76W05
  • DOI:
  • MathSciNet review: 2813340