A novel approach to study the wellposedness of the 3D fluid-2D plate interaction PDE System
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909769046949888 |
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| author | Avalos, George Geredeli, Pelin G. Kunwar, Hemanta Lee, Hyesuk |
| author_facet | Avalos, George Geredeli, Pelin G. Kunwar, Hemanta Lee, Hyesuk |
| contents | We consider a certain fluid-structure interaction (FSI) system with a view of obtaining an alternative methodology for establishing its strongly continuous semigroup wellposedness. (Semigroup generation for this FSI was originally considered in Avalos-Clark (2014).) The FSI model under consideration describes the vibrations of an incompressible fluid within a 3D cavity as it interacts with the elastic membrane on the ``free" upper boundary of the cavity. Such coupled PDE systems appear in variety of natural settings such as biomedicine, aeroelasticity, and fluid dynamics.
Our proof of $C_0$-semigroup wellposedness is based on a proper application of Lumer Phillips Theorem. In this regard, our main challenge is to show the maximality of the corresponding semigroup generator. To this end, we develop a ``nonstandard" inf-sup approach which avoids the use of technical nonlocal maps in the associated bilinear forms--unlike the earlier paper Avalos-Clark (2014)--and allows for the solution of the fluid and plate solution variables simultanously. Our new inf-sup strategy will lead to a more efficient mixed finite element method (FEM) for approximating solutions to the FSI problem, inasmuch our novel variational formulation avoids bilinear forms which are free from the computationally-intensive nonlocal solution operators invoked in Avalos-Clark (2014). We also perform numerical tests based on this formulation using a benchmark problem
and present numerical results to demonstrate the effectiveness of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A novel approach to study the wellposedness of the 3D fluid-2D plate interaction PDE System Avalos, George Geredeli, Pelin G. Kunwar, Hemanta Lee, Hyesuk Analysis of PDEs Numerical Analysis 35Q25 (Primary), 65N30, 35A01, 74K20, 76M10 (Secondary) We consider a certain fluid-structure interaction (FSI) system with a view of obtaining an alternative methodology for establishing its strongly continuous semigroup wellposedness. (Semigroup generation for this FSI was originally considered in Avalos-Clark (2014).) The FSI model under consideration describes the vibrations of an incompressible fluid within a 3D cavity as it interacts with the elastic membrane on the ``free" upper boundary of the cavity. Such coupled PDE systems appear in variety of natural settings such as biomedicine, aeroelasticity, and fluid dynamics. Our proof of $C_0$-semigroup wellposedness is based on a proper application of Lumer Phillips Theorem. In this regard, our main challenge is to show the maximality of the corresponding semigroup generator. To this end, we develop a ``nonstandard" inf-sup approach which avoids the use of technical nonlocal maps in the associated bilinear forms--unlike the earlier paper Avalos-Clark (2014)--and allows for the solution of the fluid and plate solution variables simultanously. Our new inf-sup strategy will lead to a more efficient mixed finite element method (FEM) for approximating solutions to the FSI problem, inasmuch our novel variational formulation avoids bilinear forms which are free from the computationally-intensive nonlocal solution operators invoked in Avalos-Clark (2014). We also perform numerical tests based on this formulation using a benchmark problem and present numerical results to demonstrate the effectiveness of our approach. |
| title | A novel approach to study the wellposedness of the 3D fluid-2D plate interaction PDE System |
| topic | Analysis of PDEs Numerical Analysis 35Q25 (Primary), 65N30, 35A01, 74K20, 76M10 (Secondary) |
| url | https://arxiv.org/abs/2509.03431 |