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dc.contributor.advisorVishik, Mikhailen
dc.creatorCozzi, Elaine Marie, 1978-en
dc.date.accessioned2008-08-28T23:32:50Zen
dc.date.available2008-08-28T23:32:50Zen
dc.date.issued2007-08en
dc.identifierb68787893en
dc.identifier.urihttp://hdl.handle.net/2152/3191en
dc.descriptiontexten
dc.description.abstractIn this thesis, we consider soltions to the two-dimensional Euler equations with uniformly continuous initial vorticity in a critical or subcritical Besov space. We use paradifferential calculus to show that the solution will lose an arbitrarily small amount of smoothness over any fixed finite time interval. This result is motivated by a theorem of Bahouri and Chemin which states that the Sobolev exponent of a solution to the two-dimensional Euler equations in a critical or subcritical Sobolev space may decay exponentially with time. To prove our result, one can use methods similar to those used by Bahouri and Chemin for initial vorticity in a Besov space with Besov exponent between 0 and 1; however, we use different methods to prove a result which applies for any Sobolev exponent between 0 and 2. The remainder of this thesis is based on joint work with J. Kelliher. We study the vanishing viscosity limit of solutions of the Navier-Stokes equations to solutions of the Euler equations in the plane assuming initial vorticity is in a variant Besov space introduced by Vishik. Our methods allow us to extend a global in time uniqueness result established by Vishik for the two-dimensional Euler equations in this space.en
dc.format.mediumelectronicen
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshDifferential equations, Partial--Numerical solutionsen
dc.subject.lcshNavier-Stokes equations--Numerical solutionsen
dc.subject.lcshBesov spacesen
dc.titleIncompressible fluids with vorticity in Besov spacesen
dc.description.departmentMathematicsen
dc.identifier.oclc173621144en
dc.type.genreThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen


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