{"id":{"repo_id":"uic","oai_identifier":"oai:figshare.com:article/30426316"},"canonical_url":"https://search.dev.ndltd.org/etd/uic/oai:figshare.com:article/30426316","repository":{"repo_id":"uic","name":"University of Illinois - Chicago","base_url":"https://api.figshare.com/v2/oai"},"display":{"title":"Regularity of Solution Maps of the Generalized Surface Quasi-Geostrophic Equations","abstract":"In Chapter 1, we present some preliminaries. In Chapter 2 we drive generalized SQG equations as Euler-Arnold equations. Chapter 3, we establish analyticity of the exponential map associated to the generalized SQG equations. In Chapter 4, we establish that the Eulerian data-to-solution map for the generalized SQG equations fails to be uniformly continuous in Sobolev spaces.","abstract_html":"In Chapter 1, we present some preliminaries. In Chapter 2 we drive generalized SQG equations as Euler-Arnold equations. Chapter 3, we establish analyticity of the exponential map associated to the generalized SQG equations. In Chapter 4, we establish that the Eulerian data-to-solution map for the generalized SQG equations fails to be uniformly continuous in Sobolev spaces.","abstract_has_math":false,"creators":["Truong X. Vu (22483021)"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-08-01T00:00:00Z","date_published":"2025-08-01T00:00:00Z","updated_at":"2026-07-27T21:34:55Z","subjects":["Mathematics"],"languages":[],"rights":["In Copyright","Open Access after 2027-09-01"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.25417/uic.30426316.v1","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Truong X. Vu (22483021)"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-08-01T00:00:00Z"]},{"key":"dc:relation","label":"Dc Relation","values":["https://figshare.com/articles/thesis/Regularity_of_Solution_Maps_of_the_Generalized_Surface_Quasi-Geostrophic_Equations/30426316"]},{"key":"dc:type","label":"Dc Type","values":["Text","Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright","Open Access after 2027-09-01"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.25417/uic.30426316.v1"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In Chapter 1, we present some preliminaries. In Chapter 2 we drive generalized SQG equations as Euler-Arnold equations. Chapter 3, we establish analyticity of the exponential map associated to the generalized SQG equations. In Chapter 4, we establish that the Eulerian data-to-solution map for the generalized SQG equations fails to be uniformly continuous in Sobolev spaces."]},{"key":"dc:title","label":"Title","values":["Regularity of Solution Maps of the Generalized Surface Quasi-Geostrophic Equations"]}]}],"canonical_facts":{"dc:creator":["Truong X. Vu (22483021)"],"dc:date":["2025-08-01T00:00:00Z"],"dc:description":["In Chapter 1, we present some preliminaries. In Chapter 2 we drive generalized SQG equations as Euler-Arnold equations. Chapter 3, we establish analyticity of the exponential map associated to the generalized SQG equations. In Chapter 4, we establish that the Eulerian data-to-solution map for the generalized SQG equations fails to be uniformly continuous in Sobolev spaces."],"dc:identifier":["10.25417/uic.30426316.v1"],"dc:relation":["https://figshare.com/articles/thesis/Regularity_of_Solution_Maps_of_the_Generalized_Surface_Quasi-Geostrophic_Equations/30426316"],"dc:rights":["In Copyright","Open Access after 2027-09-01"],"dc:subject":["Mathematics"],"dc:title":["Regularity of Solution Maps of the Generalized Surface Quasi-Geostrophic Equations"],"dc:type":["Text","Thesis"]},"updated_at":"2026-07-27T21:34:55Z"}