Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published August 7, 2006 | public
Journal Article Open

On Global Well-Posedness of the Lagrangian Averaged Euler Equations

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

HOUsiamjma06.pdf
Files (155.2 kB)
Name Size Download all
md5:f2f77d871292c825ee014d1d91810cfc
155.2 kB Preview Download

Additional details

Created:
August 22, 2023
Modified:
October 16, 2023