Published August 7, 2006
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Journal Article
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On Global Well-Posedness of the Lagrangian Averaged Euler Equations
- Creators
- Hou, Thomas Y.
- Li, Congming
Chicago
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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.
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.Files
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Additional details
- Eprint ID
- 6811
- Resolver ID
- CaltechAUTHORS:HOUsiamjma06
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2006-12-23Created from EPrint's datestamp field
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2021-11-08Created from EPrint's last_modified field