PDEA Seminar: Time-periodic solutions for fluid-structure interactions

Abstract: Under the action of a time-periodic external force we prove the existence of at least one time-periodic weak solution for the interaction between a three-dimensional incompressible fluid, governed by the Navier–Stokes equation and a two-dimensional elastic plate. The challenge is that the Eulerian domain for the fluid changes in time and is a part of the solution. We introduce a two fixed-point methodology. First we construct a time-periodic solutions for a given variable time-periodic geometry. Then in a second step a fixed point is performed w.r.t. the geometry of the domain. The existence relies on newly developed a-priori estimates applicable for both coupled and uncoupled variable geometries. Due to the expected weak regularity of the solutions such estimates are unavoidable. Note in particular that only the fluid is assumed to be dissipative, while the solid is hyperbolic. The talk is based on a joint work with C. Mindrila.

This is a seminar in the PDEs and Applications seminar series