{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-1115"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-1115","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"Backward stochastic Navier-Stokes equations in two dimensions","abstract":"There are two parts in this dissertation. The backward stochastic Lorenz system is studied in the first part. Suitable a priori estimates for adapted solutions of the backward stochastic Lorenz system are obtained. The existence and uniqueness of solutions is shown by the use of suitable truncations and approximations. The continuity of the adapted solutions with respect to the terminal data is also established. The backward stochastic Navier-Stokes equations (BSNSEs, for short) corresponding to incompressible fluid flow in a bounded domain $G$ are studied in the second part. Suitable a priori estimates for adapted solutions of the BSNSEs are obtained which reveal a surprising pathwise $L^{infty}(H)$ bound on the solutions. The existence of solutions is shown by using a monotonicity argument. Uniqueness is proved by using a novel method that uses finite-dimensional projections, linearization, and truncations. The continuity of the adapted solutions with respect to the terminal data and the external body force is also established.","abstract_html":"There are two parts in this dissertation. The backward stochastic Lorenz system is studied in the first part. Suitable a priori estimates for adapted solutions of the backward stochastic Lorenz system are obtained. The existence and uniqueness of solutions is shown by the use of suitable truncations and approximations. The continuity of the adapted solutions with respect to the terminal data is also established. The backward stochastic Navier-Stokes equations (BSNSEs, for short) corresponding to incompressible fluid flow in a bounded domain $G$ are studied in the second part. Suitable a priori estimates for adapted solutions of the BSNSEs are obtained which reveal a surprising pathwise <span class=\"etd-inline-math\">L<sup>infty</sup>(H)</span> bound on the solutions. The existence of solutions is shown by using a monotonicity argument. Uniqueness is proved by using a novel method that uses finite-dimensional projections, linearization, and truncations. The continuity of the adapted solutions with respect to the terminal data and the external body force is also established.","abstract_has_math":true,"creators":["Yin, Hong"],"institution":"Mathematics","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Applied Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2007,"date_issued":"2007-01-01T08:00:00Z","date_published":"2007-01-01T08:00:00Z","updated_at":"2026-07-24T02:57:12Z","subjects":["Backward stochastic Navier-Stokes equations","Lorenz system","Gronwall inequality","Truncated system","Galerkin approximation"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-04122007-145924","https://repository.lsu.edu/gradschool_dissertations/116"],"render_values":[{"text":"etd-04122007-145924","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/116","href":"https://repository.lsu.edu/gradschool_dissertations/116","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.116","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Yin, Hong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2007-04-09"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:07:44Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Backward stochastic Navier-Stokes equations","Lorenz system","Gronwall inequality","Truncated system","Galerkin approximation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-04122007-145924","10.31390/gradschool_dissertations.116","https://repository.lsu.edu/gradschool_dissertations/116"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["There are two parts in this dissertation. The backward stochastic Lorenz system is studied in the first part. Suitable a priori estimates for adapted solutions of the backward stochastic Lorenz system are obtained. The existence and uniqueness of solutions is shown by the use of suitable truncations and approximations. The continuity of the adapted solutions with respect to the terminal data is also established. The backward stochastic Navier-Stokes equations (BSNSEs, for short) corresponding to incompressible fluid flow in a bounded domain $G$ are studied in the second part. Suitable a priori estimates for adapted solutions of the BSNSEs are obtained which reveal a surprising pathwise $L^{infty}(H)$ bound on the solutions. The existence of solutions is shown by using a monotonicity argument. Uniqueness is proved by using a novel method that uses finite-dimensional projections, linearization, and truncations. The continuity of the adapted solutions with respect to the terminal data and the external body force is also established."]},{"key":"dc:title","label":"Title","values":["Backward stochastic Navier-Stokes equations in two dimensions"]}]}],"canonical_facts":{"dc:creator":["Yin, Hong"],"dc:date":["2007-04-09"],"dc:date.available":["2022-05-12T23:07:44Z"],"dc:description.abstract":["There are two parts in this dissertation. The backward stochastic Lorenz system is studied in the first part. Suitable a priori estimates for adapted solutions of the backward stochastic Lorenz system are obtained. The existence and uniqueness of solutions is shown by the use of suitable truncations and approximations. The continuity of the adapted solutions with respect to the terminal data is also established. The backward stochastic Navier-Stokes equations (BSNSEs, for short) corresponding to incompressible fluid flow in a bounded domain $G$ are studied in the second part. Suitable a priori estimates for adapted solutions of the BSNSEs are obtained which reveal a surprising pathwise $L^{infty}(H)$ bound on the solutions. The existence of solutions is shown by using a monotonicity argument. Uniqueness is proved by using a novel method that uses finite-dimensional projections, linearization, and truncations. The continuity of the adapted solutions with respect to the terminal data and the external body force is also established."],"dc:identifier":["etd-04122007-145924","10.31390/gradschool_dissertations.116","https://repository.lsu.edu/gradschool_dissertations/116"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["Backward stochastic Navier-Stokes equations","Lorenz system","Gronwall inequality","Truncated system","Galerkin approximation"],"dc:title":["Backward stochastic Navier-Stokes equations in two dimensions"],"thesis:degree_discipline":["Applied Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Mathematics"]},"updated_at":"2026-07-24T02:57:12Z"}