Global Regularity for Euler Vortex Patch in Bounded Smooth Domains

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dc.contributor.advisorKiselev, Alexander
dc.contributor.committeeMemberHardt, Robert
dc.creatorLi, Chao
dc.date.accessioned2019-05-17T15:11:02Z
dc.date.available2019-05-17T15:11:02Z
dc.date.created2018-05
dc.date.issued2018-04-18
dc.date.submittedMay 2018
dc.date.updated2019-05-17T15:11:03Z
dc.description.abstractIt is well known that the Euler vortex patch in two dimensional plane will remain regular if it is regular enough initially. In bounded domains, the regularity theory for patch solutions is less complete. In this thesis, I study the Euler vortex patch in a general smooth bounded domain. I prove global in time regularity by providing the upper bound of the growth on curvature of the patch boundary. For a special symmetric scenario, I construct an example of double exponential curvature growth, showing that our upper bound is qualitatively sharp.
dc.format.mimetypeapplication/pdf
dc.identifier.citationLi, Chao. "Global Regularity for Euler Vortex Patch in Bounded Smooth Domains." (2018) Diss., Rice University. <a href="https://hdl.handle.net/1911/105752">https://hdl.handle.net/1911/105752</a>.
dc.identifier.urihttps://hdl.handle.net/1911/105752
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectEuler vortex patch
dc.subjectglobal regularity
dc.subjectbounded smooth domain
dc.titleGlobal Regularity for Euler Vortex Patch in Bounded Smooth Domains
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematics
thesis.degree.disciplineNatural Sciences
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.majorPartial Differential Equations
thesis.degree.nameDoctor of Philosophy
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