Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Professor Frederic Marbach, University of Rennes, France
Inviter:
Title:
Controllability despite boundary layers
Time & Venue:
2018.5.4 15:00-17:00 N913
Abstract:
Controllability is the question of whether one can find a source-term (the control) to drive the solution of an evolution equation from a given initial state to a prescribed final state. In this lecture, we will study the question of controllability in small time for systems coming from fluid mechanics (Burgers, Navier-Stokes). I will explain why answering this question implies understanding the behavior of boundary layers. Several usual techniques will be used: asymptotic expansions, Coron's return method, energy estimates (Sobolev or analytic). I will also explain a recent technique to build controls that enhance the dissipation of the involved boundary layers.