Kiselev, Alexander2019-05-172019-05-172018-052018-04-18May 2018Li, 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>.https://hdl.handle.net/1911/105752It 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.application/pdfengCopyright 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.Euler vortex patchglobal regularitybounded smooth domainThesis2019-05-17