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On Global Well-Posedness of the Lagrangian Averaged Euler Equations

Hou, Thomas Y. and Li, Congming (2006) On Global Well-Posedness of the Lagrangian Averaged Euler Equations. SIAM Journal on Mathematical Analysis, 38 (3). pp. 782-794. ISSN 0036-1410. https://resolver.caltech.edu/CaltechAUTHORS:HOUsiamjma06

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Abstract

We study the global well-posedness of the Lagrangian averaged Euler equations in three dimensions. We show that a necessary and sufficient condition for the global existence is that the bounded mean oscillation of the stream function is integrable in time. We also derive a sufficient condition in terms of the total variation of certain level set functions, which guarantees the global existence. Furthermore, we obtain the global existence of the averaged two-dimensional (2D) Boussinesq equations and the Lagrangian averaged 2D quasi-geostrophic equations in finite Sobolev space in the absence of viscosity or dissipation.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1137/050625783DOIUNSPECIFIED
Additional Information:©2006 Society for Industrial and Applied Mathematics (Received March 2, 2005; accepted February 7, 2006; published August 7, 2006) This author’s []T.Y.H.] research was supported in part by the National Science Foundation under FRG grant DMS-0353838 and ITR grant ACI-0204932. This author’s [C.L.] research was supported in part by the National Science Foundation under grant DMS-0401174.
Subject Keywords:well-posedness; nonlinearity partial differential equations; Euler equations
Issue or Number:3
Record Number:CaltechAUTHORS:HOUsiamjma06
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:HOUsiamjma06
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6811
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:23 Dec 2006
Last Modified:02 Oct 2019 23:36

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