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Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Convex integration for a class of active scalar equations


Author: R. Shvydkoy
Journal: J. Amer. Math. Soc. 24 (2011), 1159-1174
MSC (2010): Primary 35Q35; Secondary 76W05
Published electronically: June 6, 2011
MathSciNet review: 2813340
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Abstract: 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: shvydkoy@math.uic.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2011-00705-4
PII: S 0894-0347(2011)00705-4
Received by editor(s): October 25, 2010
Published electronically: June 6, 2011
Additional Notes: The work was partially supported by NSF grant DMS – 0907812
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.