DE Seminar: Ellie Gurvich
Graduate Students
Location
Mathematics/Psychology : 401
Date & Time
March 11, 2024, 11:00 am – 12:00 pm
Description
Title: Weak and Strong Solutions for a Fluid-Poroelastic-Stucture Interaction via a Semigroup Approach
Speaker: Ellie Gurvich
Abstract: A filtration system, comprising a Biot poroelastic solid coupled to an incompressible Stokes free-flow, is considered in 3D. Across the 2D interface, the Beavers-Joseph-Saffman coupling conditions are enforced. A semigroup approach circumvents typical issues associated with mismatched trace regularities at the interface. The linear hyperbolic-parabolic coupled problem in the fully inertial and non-degenerate case is posed through a dynamics operator on an appropriate energy space. Strong and generalized solutions are obtained via $C_0$-semigroup generation for the dynamics operator. A standard argument by density is shown to yield weak solutions, including the degenerate cases where the Biot compressibility of the constituents vanishes. Thus, for the inertial Biot-Stokes filtration, we provide a clear elucidation of strong and weak solutions and their regularity with associated energy estimates.
Abstract: A filtration system, comprising a Biot poroelastic solid coupled to an incompressible Stokes free-flow, is considered in 3D. Across the 2D interface, the Beavers-Joseph-Saffman coupling conditions are enforced. A semigroup approach circumvents typical issues associated with mismatched trace regularities at the interface. The linear hyperbolic-parabolic coupled problem in the fully inertial and non-degenerate case is posed through a dynamics operator on an appropriate energy space. Strong and generalized solutions are obtained via $C_0$-semigroup generation for the dynamics operator. A standard argument by density is shown to yield weak solutions, including the degenerate cases where the Biot compressibility of the constituents vanishes. Thus, for the inertial Biot-Stokes filtration, we provide a clear elucidation of strong and weak solutions and their regularity with associated energy estimates.
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