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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Log-log convexity and backward uniqueness


Author: Igor Kukavica
Journal: Proc. Amer. Math. Soc. 135 (2007), 2415-2421
MSC (2000): Primary 35B42, 35B41, 35K55, 35K15, 35G20
Published electronically: March 14, 2007
MathSciNet review: 2302562
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Abstract | References | Similar Articles | Additional Information

Abstract: We study backward uniqueness properties for equations of the form

$\displaystyle u' + A u = f. $

Under mild regularity assumptions on $ A$ and $ f$, it is shown that $ u(0)=0$ implies $ u(t)=0$ for $ t<0$. The argument is based on $ \alpha$-log and log-log convexity. The results apply to mildly nonlinear parabolic equations and systems with rough coefficients and the 2D Navier-Stokes system.


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Additional Information

Igor Kukavica
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
Email: kukavica@usc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08991-5
PII: S 0002-9939(07)08991-5
Keywords: Backward uniqueness, logarithmic convexity, Navier-Stokes equations
Received by editor(s): November 1, 2004
Received by editor(s) in revised form: August 30, 2005
Published electronically: March 14, 2007
Additional Notes: The author was supported in part by the NSF grant DMS-0306586
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2007 American Mathematical Society