Weak and Strong Solutions for A Fluid-Poroelastic-Structure Interaction via A Semigroup Approach
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914715253342208 |
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| author | Avalos, George Gurvich, Elena Webster, Justin T. |
| author_facet | Avalos, George Gurvich, Elena Webster, Justin T. |
| contents | A filtration system, comprising a Biot poroelastic solid coupled to an incompressible Stokes free-flow, is considered in 3D. Across the flat 2D interface, the Beavers-Joseph-Saffman coupling conditions are taken. In the inertial, linear, and non-degenerate case, the hyperbolic-parabolic coupled problem is posed through a dynamics operator on an appropriate energy space, adapted from Stokes-Lamé coupled dynamics. A semigroup approach is utilized to circumvent issues associated to mismatched trace regularities at the interface. $C_0$-semigroup generation for the dynamics operator is obtained with a non-standard maximality argument. The latter employs a mixed-variational formulation in order to invoke the Babuška-Brezzi theorem. The Lumer-Philips theorem yields semigroup generation, and thereby, strong and generalized solutions are obtained. As the dynamics are linear, a standard argument by density obtains weak solutions; we extend this argument to the case where the Biot compressibility of constituents degenerates. Thus, for the inertial Biot-Stokes filtration, we provide a clear elucidation of strong and weak solutions, as well as their regularity through associated estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03897 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak and Strong Solutions for A Fluid-Poroelastic-Structure Interaction via A Semigroup Approach Avalos, George Gurvich, Elena Webster, Justin T. Analysis of PDEs 74F10, 76S05, 35M13, 76M30, 35D30 A filtration system, comprising a Biot poroelastic solid coupled to an incompressible Stokes free-flow, is considered in 3D. Across the flat 2D interface, the Beavers-Joseph-Saffman coupling conditions are taken. In the inertial, linear, and non-degenerate case, the hyperbolic-parabolic coupled problem is posed through a dynamics operator on an appropriate energy space, adapted from Stokes-Lamé coupled dynamics. A semigroup approach is utilized to circumvent issues associated to mismatched trace regularities at the interface. $C_0$-semigroup generation for the dynamics operator is obtained with a non-standard maximality argument. The latter employs a mixed-variational formulation in order to invoke the Babuška-Brezzi theorem. The Lumer-Philips theorem yields semigroup generation, and thereby, strong and generalized solutions are obtained. As the dynamics are linear, a standard argument by density obtains weak solutions; we extend this argument to the case where the Biot compressibility of constituents degenerates. Thus, for the inertial Biot-Stokes filtration, we provide a clear elucidation of strong and weak solutions, as well as their regularity through associated estimates. |
| title | Weak and Strong Solutions for A Fluid-Poroelastic-Structure Interaction via A Semigroup Approach |
| topic | Analysis of PDEs 74F10, 76S05, 35M13, 76M30, 35D30 |
| url | https://arxiv.org/abs/2401.03897 |