Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem
<p>We study a nonlinear stochastic fluid-structure interaction problem with a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a 2D cylinder interacting with an elastic lateral wall whose elastod...
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2025
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| _version_ | 1852023085998276608 |
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| author | Krutika Tawri (20653128) |
| author2 | Sunčica Čanić (20161463) |
| author2_role | author |
| author_facet | Krutika Tawri (20653128) Sunčica Čanić (20161463) |
| author_role | author |
| dc.creator.none.fl_str_mv | Krutika Tawri (20653128) Sunčica Čanić (20161463) |
| dc.date.none.fl_str_mv | 2025-02-02T00:20:15Z |
| dc.identifier.none.fl_str_mv | 10.6084/m9.figshare.28329405.v1 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/dataset/Existence_of_martingale_solutions_to_a_nonlinearly_coupled_stochastic_fluid-structure_interaction_problem/28329405 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Biophysics Biotechnology Ecology Plant Biology Computational Biology Mathematical Sciences not elsewhere classified Physical Sciences not elsewhere classified Fluid-structure interaction martingale solutions stochastic moving boundary problems 60H15 35A01 |
| dc.title.none.fl_str_mv | Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem |
| dc.type.none.fl_str_mv | Dataset info:eu-repo/semantics/publishedVersion dataset |
| description | <p>We study a nonlinear stochastic fluid-structure interaction problem with a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a 2D cylinder interacting with an elastic lateral wall whose elastodynamics is described by a membrane equation. The flow is driven by the inlet and outlet data and by the stochastic forcing. The noise is applied both to the fluid equations as a volumetric body force, and to the structure as an external forcing to the deformable fluid boundary. The fluid and the structure are <b>nonlinearly coupled</b> via the kinematic and dynamic conditions assumed at the moving interface, which is a random variable not known <i>a priori</i>. The geometric nonlinearity due to the nonlinear coupling requires the development of new techniques to capture martingale solutions for this class of stochastic FSI problems. Our analysis reveals a first-of-its-kind temporal regularity result for the solutions. This is the first result in the field of SPDEs that addresses the existence of solutions on moving domains involving incompressible fluids, where <b>the displacement of the boundary and the fluid domain are random variables that are not known <i>a priori</i> and are parts of the solution itself</b>.</p> |
| eu_rights_str_mv | openAccess |
| id | Manara_ee5ec8cdadc8607e8cd906fabbb94065 |
| identifier_str_mv | 10.6084/m9.figshare.28329405.v1 |
| network_acronym_str | Manara |
| network_name_str | ManaraRepo |
| oai_identifier_str | oai:figshare.com:article/28329405 |
| publishDate | 2025 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problemKrutika Tawri (20653128)Sunčica Čanić (20161463)BiophysicsBiotechnologyEcologyPlant BiologyComputational BiologyMathematical Sciences not elsewhere classifiedPhysical Sciences not elsewhere classifiedFluid-structure interactionmartingale solutionsstochastic moving boundary problems60H1535A01<p>We study a nonlinear stochastic fluid-structure interaction problem with a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a 2D cylinder interacting with an elastic lateral wall whose elastodynamics is described by a membrane equation. The flow is driven by the inlet and outlet data and by the stochastic forcing. The noise is applied both to the fluid equations as a volumetric body force, and to the structure as an external forcing to the deformable fluid boundary. The fluid and the structure are <b>nonlinearly coupled</b> via the kinematic and dynamic conditions assumed at the moving interface, which is a random variable not known <i>a priori</i>. The geometric nonlinearity due to the nonlinear coupling requires the development of new techniques to capture martingale solutions for this class of stochastic FSI problems. Our analysis reveals a first-of-its-kind temporal regularity result for the solutions. This is the first result in the field of SPDEs that addresses the existence of solutions on moving domains involving incompressible fluids, where <b>the displacement of the boundary and the fluid domain are random variables that are not known <i>a priori</i> and are parts of the solution itself</b>.</p>2025-02-02T00:20:15ZDatasetinfo:eu-repo/semantics/publishedVersiondataset10.6084/m9.figshare.28329405.v1https://figshare.com/articles/dataset/Existence_of_martingale_solutions_to_a_nonlinearly_coupled_stochastic_fluid-structure_interaction_problem/28329405CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/283294052025-02-02T00:20:15Z |
| spellingShingle | Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem Krutika Tawri (20653128) Biophysics Biotechnology Ecology Plant Biology Computational Biology Mathematical Sciences not elsewhere classified Physical Sciences not elsewhere classified Fluid-structure interaction martingale solutions stochastic moving boundary problems 60H15 35A01 |
| status_str | publishedVersion |
| title | Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem |
| title_full | Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem |
| title_fullStr | Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem |
| title_full_unstemmed | Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem |
| title_short | Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem |
| title_sort | Existence of martingale solutions to a nonlinearly coupled stochastic fluid-structure interaction problem |
| topic | Biophysics Biotechnology Ecology Plant Biology Computational Biology Mathematical Sciences not elsewhere classified Physical Sciences not elsewhere classified Fluid-structure interaction martingale solutions stochastic moving boundary problems 60H15 35A01 |