PDE Seminar Abstracts

PDE systems describing the motion of solids in a viscous fluid: wellposedness, control and long-time behaviour

Marius Tucsnac
University of Bordeaux, France
Wed 1st Nov 2023, 10-11am, Carslaw Room 829 (AGR)


The study of systems describing the motion of rigid bodies in a fluid goes back to Euler and Kirchhoff, who considered the case of an ideal fluid subject undergoing a potential flow. The case of a single solid moving in a viscous incompressible fluid filling the whole space was considered much later, around 1980 by Weinberger and Serre. Welposedness issues for the case when the solid-fluid system is contained in a bounded container or/and of several moving bodies has been intensively studied since 2000. In this talk we first recall some of these wellposedness results . We next describe some associated control problems, aimed to provide a new approach to the understanding of the swimming of aquatic organisms. We finally describe some recent results concerning the long-time behaviour of solutions.The celebrated hot spots conjecture says that the second Neumann eigenfunctions attain their (global) maximum (hottest point) only on the boundary of the domain.