【ハイブリッド開催】東工大 数理解析セミナー： Franck Sueur 氏
- Lagrangian controllability of the incompressible Navier-Stokes equations
- The talk will be devoted to the issue of the Lagrangian controllability in incompressible fluid mechanics, which consists in driving, by a remote action, a closed patch of particles of an incompressible fluid, from a given initial place to another given targeted final place. A natural setting is the case where the fluid occupies an open bounded domain, with an impermeability condition on the boundary except on an open non-void subset where an appropriate boundary data can be chosen freely as a boundary control. Another typical requirement in Lagrangian controllability is that the patch particles do no go out of the domain during the process, which forbids a quite undesired total flush, on the opposite to the more classical Eulerian controllability problem, as promoted by J.-L. Lions in the 80’s. We will review some earlier and recent advances in this direction and will advertise an ongoing joint work with Ludovick Gagnon, Toan T. Nguyen and Trinh T. Nguyen, on the case of the 2D incompressible Navier-Stokes equations.