Analysis and PDE Seminar—— Controllability of the Navier-Stokes equation in a rectangle with a little help of a phantom force
主 题: Analysis and PDE Seminar—— Controllability of the Navier-Stokes equation in a rectangle with a little help of a phantom force
报告人: Frédéric Marbach (ENS Rennes)
时 间: 2018-04-27 14:30-15:30
地 点: Room 1418, Sciences Building No. 1
Abstract: In this joint work with Jean-Michel Coron, Franck Sueur and Ping Zhang, we consider the incompressible Navier-Stokes equation in a rectangle, with null no-slip Dirichlet boundary conditions on the lower and upper boundaries. We prove that, for any large initial data, for any small time, there exists boundary controls on the left and right walls and a very small distributed force, such that the corresponding solution is at rest at the final time. I will explain how the proof mixes an initial enhanced regularization of the initial data, the well-prepared dissipation of a boundary layer and a long-time Cauchy-Kowalevski estimate.
