Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the radius of analyticity of solutions to the three-dimensional Euler equations


Authors: Igor Kukavica and Vlad Vicol
Journal: Proc. Amer. Math. Soc. 137 (2009), 669-677
MSC (2000): Primary 76B03, 35L60
DOI: https://doi.org/10.1090/S0002-9939-08-09693-7
Published electronically: September 16, 2008
MathSciNet review: 2448589
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We address the problem of analyticity of smooth solutions $u$ of the incompressible Euler equations. If the initial datum is real–analytic, the solution remains real–analytic as long as $\int _{0}^{t} \left \Vert {\nabla u(\cdot ,s)}\right \Vert _{L^\infty } ds< \infty$. Using a Gevrey-class approach we obtain lower bounds on the radius of space analyticity which depend algebraically on $\exp {\int _{0}^{t} \left \Vert {\nabla u(\cdot ,s)}\right \Vert _{L^\infty }}ds$. In particular, we answer in the positive a question posed by Levermore and Oliver.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 76B03, 35L60

Retrieve articles in all journals with MSC (2000): 76B03, 35L60


Additional Information

Igor Kukavica
Affiliation: Department of Mathematics, University of Southern California, 3620 S. Vermont Avenue, Los Angeles, California 90089
MR Author ID: 314775
Email: kukavica@usc.edu

Vlad Vicol
Affiliation: Department of Mathematics, University of Southern California, 3620 S. Vermont Avenue, Los Angeles, California 90089
MR Author ID: 846012
ORCID: setImmediate$0.00243841196800898$2
Email: vicol@usc.edu

Received by editor(s): November 13, 2007
Published electronically: September 16, 2008
Additional Notes: Both authors were supported in part by the NSF grant DMS-0604886.
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2008 American Mathematical Society