{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/24775"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/24775","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Taming of Complex Dynamical Systems","abstract":"The problem of establishing local existence and uniqueness of solutions to systems of differential equations is well understood and has a long history. However, the problem of proving global existence and uniqueness is more difficult and fails even for some very simple ordinary differential equations. It is still not known if the 3D Navier-Stokes equation have global unique solutions and this open problem is one of the Millennium Prize Problems. However, many of these mathematical models are extremely useful in the understanding of complex physical systems. For years people have considered methods for modifying these equations in order to obtain models that still capture the observed fundamental physics, but for which one can rigorously establish global results. In this thesis we focus on a taming method to achieve this goal and apply taming to modeling and numerical problems. The method is also applied to a class of nonlinear differential equations with conservative nonlinearities and to Burgers’ Equation with Neumann boundary conditions. Numerical results are presented to illustrate the ideas.","abstract_html":"The problem of establishing local existence and uniqueness of solutions to systems of differential equations is well understood and has a long history. However, the problem of proving global existence and uniqueness is more difficult and fails even for some very simple ordinary differential equations. It is still not known if the 3D Navier-Stokes equation have global unique solutions and this open problem is one of the Millennium Prize Problems. However, many of these mathematical models are extremely useful in the understanding of complex physical systems. For years people have considered methods for modifying these equations in order to obtain models that still capture the observed fundamental physics, but for which one can rigorously establish global results. In this thesis we focus on a taming method to achieve this goal and apply taming to modeling and numerical problems. The method is also applied to a class of nonlinear differential equations with conservative nonlinearities and to Burgers’ Equation with Neumann boundary conditions. Numerical results are presented to illustrate the ideas.","abstract_has_math":false,"creators":["Grimm, Alexander Rudolf"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Burns, John A."],"committee_members":["Zietsman, Lizette","Gugercin, Serkan"],"year":2013,"date_issued":"2013-12-31","date_published":"2013-12-31","updated_at":"2026-07-22T22:19:44Z","subjects":["Taming","Dynamical Systems","Navier Stokes","Burgers Equation","Finite Elements"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:1574"],"render_values":[{"text":"vt_gsexam:1574","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/24775","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Burns, John A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Zietsman, Lizette","Gugercin, Serkan"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Grimm, Alexander Rudolf"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-01-01T09:00:09Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-01-01T09:00:09Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-12-31"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Taming","Dynamical Systems","Navier Stokes","Burgers Equation","Finite Elements"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:1574"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/24775"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The problem of establishing local existence and uniqueness of solutions to systems of differential equations is well understood and has a long history. However, the problem of proving global existence and uniqueness is more difficult and fails even for some very simple ordinary differential equations. It is still not known if the 3D Navier-Stokes equation have global unique solutions and this open problem is one of the Millennium Prize Problems. However, many of these mathematical models are extremely useful in the understanding of complex physical systems. For years people have considered methods for modifying these equations in order to obtain models that still capture the observed fundamental physics, but for which one can rigorously establish global results. In this thesis we focus on a taming method to achieve this goal and apply taming to modeling and numerical problems. The method is also applied to a class of nonlinear differential equations with conservative nonlinearities and to Burgers’ Equation with Neumann boundary conditions. Numerical results are presented to illustrate the ideas."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Taming of Complex Dynamical Systems"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Burns, John A."],"dc:contributor.committeemember":["Zietsman, Lizette","Gugercin, Serkan"],"dc:contributor.department":["Mathematics"],"dc:creator":["Grimm, Alexander Rudolf"],"dc:date.accessioned":["2014-01-01T09:00:09Z"],"dc:date.available":["2014-01-01T09:00:09Z"],"dc:date.issued":["2013-12-31"],"dc:description.abstract":["The problem of establishing local existence and uniqueness of solutions to systems of differential equations is well understood and has a long history. However, the problem of proving global existence and uniqueness is more difficult and fails even for some very simple ordinary differential equations. It is still not known if the 3D Navier-Stokes equation have global unique solutions and this open problem is one of the Millennium Prize Problems. However, many of these mathematical models are extremely useful in the understanding of complex physical systems. For years people have considered methods for modifying these equations in order to obtain models that still capture the observed fundamental physics, but for which one can rigorously establish global results. In this thesis we focus on a taming method to achieve this goal and apply taming to modeling and numerical problems. The method is also applied to a class of nonlinear differential equations with conservative nonlinearities and to Burgers’ Equation with Neumann boundary conditions. Numerical results are presented to illustrate the ideas."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:1574"],"dc:identifier.uri":["http://hdl.handle.net/10919/24775"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Taming","Dynamical Systems","Navier Stokes","Burgers Equation","Finite Elements"],"dc:title":["Taming of Complex Dynamical Systems"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:44Z"}