{"id":{"repo_id":"maryland","oai_identifier":"oai:drum.lib.umd.edu:1903/24912"},"canonical_url":"https://search.dev.ndltd.org/etd/maryland/oai:drum.lib.umd.edu:1903/24912","repository":{"repo_id":"maryland","name":"University of Maryland","base_url":"https://api.drum.lib.umd.edu/server/oai/request"},"display":{"title":"BESOV WE11-POSEDNESS FOR HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS","abstract":"Following work of Tataru, [13] and [11], we solve the division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that non-linear wave equations which can be written as systems involving equations of the form Φ = Φ∇Φ and Φ = |∇Φ|^2 are well-posed with scattering in (6+1) and higher dimensions if the Cauchy data are small in the scale invariant ℓ^1 Besov space B^sc,1.","abstract_html":"Following work of Tataru, [13] and [11], we solve the division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that non-linear wave equations which can be written as systems involving equations of the form Φ = Φ∇Φ and Φ = |∇Φ|^2 are well-posed with scattering in (6+1) and higher dimensions if the Cauchy data are small in the scale invariant ℓ^1 Besov space B^sc,1.","abstract_has_math":false,"creators":["Sterbenz, Jacob"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Mathematics","school":null,"contributors":[],"advisors":["Machedon, Matei"],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003","date_published":"2003","updated_at":"2026-07-24T03:02:10Z","subjects":[],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.13016/ky8p-tfuz"],"render_values":[{"text":"https://doi.org/10.13016/ky8p-tfuz","href":"https://doi.org/10.13016/ky8p-tfuz","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1903/24912","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Machedon, Matei"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Sterbenz, Jacob"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-09-25T16:49:43Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2019-09-25T16:49:43Z"]},{"key":"dc:date.issued","label":"Date","values":["2003"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.13016/ky8p-tfuz"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1903/24912"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Following work of Tataru, [13] and [11], we solve the division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that non-linear wave equations which can be written as systems involving equations of the form Φ = Φ∇Φ and Φ = |∇Φ|^2 are well-posed with scattering in (6+1) and higher dimensions if the Cauchy data are small in the scale invariant ℓ^1 Besov space B^sc,1."]},{"key":"dc:title","label":"Title","values":["BESOV WE11-POSEDNESS FOR HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS"]}]}],"canonical_facts":{"dc:contributor.advisor":["Machedon, Matei"],"dc:contributor.department":["Mathematics"],"dc:creator":["Sterbenz, Jacob"],"dc:date.accessioned":["2019-09-25T16:49:43Z"],"dc:date.available":["2019-09-25T16:49:43Z"],"dc:date.issued":["2003"],"dc:description.abstract":["Following work of Tataru, [13] and [11], we solve the division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that non-linear wave equations which can be written as systems involving equations of the form Φ = Φ∇Φ and Φ = |∇Φ|^2 are well-posed with scattering in (6+1) and higher dimensions if the Cauchy data are small in the scale invariant ℓ^1 Besov space B^sc,1."],"dc:identifier":["https://doi.org/10.13016/ky8p-tfuz"],"dc:identifier.uri":["http://hdl.handle.net/1903/24912"],"dc:language.iso":["en_US"],"dc:title":["BESOV WE11-POSEDNESS FOR HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T03:02:10Z"}