{"id":{"repo_id":"rice","oai_identifier":"oai:repository.rice.edu:1911/105752"},"canonical_url":"https://search.dev.ndltd.org/etd/rice/oai:repository.rice.edu:1911/105752","repository":{"repo_id":"rice","name":"Rice University","base_url":"https://repository.rice.edu/server/oai/request"},"display":{"title":"Global Regularity for Euler Vortex Patch in Bounded Smooth Domains","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Li, Chao"],"institution":"Rice University","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Natural Sciences","degree_department":null,"school":null,"contributors":[],"advisors":["Kiselev, Alexander"],"committee_chairs":[],"committee_members":["Hardt, Robert"],"year":2018,"date_issued":"2018-04-18","date_published":"2018-04-18","updated_at":"2026-07-24T04:10:32Z","subjects":["Euler vortex patch","global regularity","bounded smooth domain"],"languages":["eng"],"rights":["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."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1911/105752","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Kiselev, Alexander"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Hardt, Robert"]},{"key":"dc:creator","label":"Author","values":["Li, Chao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-05-17T15:11:02Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2019-05-17T15:11:02Z"]},{"key":"dc:date.issued","label":"Date","values":["2018-04-18"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Natural Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Rice University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Euler vortex patch","global regularity","bounded smooth domain"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is held by the author, unless otherwise indicated. 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For a special symmetric scenario, I construct an example of double exponential curvature growth, showing that our upper bound is qualitatively sharp."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Global Regularity for Euler Vortex Patch in Bounded Smooth Domains"]}]}],"canonical_facts":{"dc:contributor.advisor":["Kiselev, Alexander"],"dc:contributor.committeemember":["Hardt, Robert"],"dc:creator":["Li, Chao"],"dc:date.accessioned":["2019-05-17T15:11:02Z"],"dc:date.available":["2019-05-17T15:11:02Z"],"dc:date.issued":["2018-04-18"],"dc:description.abstract":["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."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/1911/105752"],"dc:language.iso":["eng"],"dc:rights":["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."],"dc:subject":["Euler vortex patch","global regularity","bounded smooth domain"],"dc:title":["Global Regularity for Euler Vortex Patch in Bounded Smooth Domains"],"dc:type":["Thesis"],"thesis:degree_discipline":["Natural Sciences"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Rice University"]},"updated_at":"2026-07-24T04:10:32Z"}