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Advanced seminar AG Mathematical Modeling
Monday, 28.10.2024 at 17.00 in B7 - 210 - Seminar room A
Lecture by Dr. Pei Su (Paris-Saclay) on the topic "Conditional regularity for an elastic shell interacting with the Navier-Stokes equations".
Abstract: We are interested in the interaction of a viscous incompressible fluid with an elastic structure, where the structure is located on a part of the fluid boundary. It reacts to the surface forces induced by the fluid and deforms the reference domain to the moving domain. The fluid equations are coupled with the structure via the kinematic condition and the action-reaction principle on the interface.
We study the 2D visco-elastic shell interacts with 3D Navier-Stokes equations. Especially in a general reference geometry (the shell deforms along the normal direction of the flexible boundary), we prove a counterpart of the classical Ladyzhenskaya-Prodi-Serrin condition yielding conditional regularity and uniqueness of a solution. This additionally requires the deformation of the shell is Lipschitz continuous.
This is based on joint work with D. Breit (Clausthal), P. Mensah (Clausthal) and S. Schwarzacher (Uppsala).