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Kiselev, Alexander Hardt, Robert Li, Chao 2019-05-17T15:11:02Z 2019-05-17T15:11:02Z 2018-05 2018-04-18 May 2018 2019-05-17T15:11:03Z Li, 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/1911/105752 It 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/pdf eng Copyright 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 patch global regularity bounded smooth domain Global Regularity for Euler Vortex Patch in Bounded Smooth Domains Thesis Text Mathematics Natural Sciences Rice University Doctoral Doctor of Philosophy Partial Differential Equations open.access