Uniform stabilization of the 3d-Navier-Stokes equations by finitedimensional, localized, boundary-based feedback controllers
主题: Uniform stabilization of the 3d-Navier-Stokes equations by finitedimensional, localized, boundary-based feedback control主讲人: Roberto Triggiani地点: 腾讯会议83302663939时间: 2020-09-19 20:00:00组织单位: 理学院
Roberto Triggiani is a Professor of University of Memphis, USA. His research field is controltheory of partial differential equations.
The study of uniform stabilization of Navier-Stokes equations byfeedback controls was initiated about 20 years ago. The following problemremained open: can the localized, boundary-based, stabilizing controls beasserted to be finite dimensional also for d=3? Prior results (2015) requiredthe additional assumption that the Initial Conditions be compactly supported.We shall provide an affirmative solution of this problem. It will require adrastic change of the functional setting from the Sobolev-Hilbert based settingof past literature to a Besov space setting with tight indeces. Moreover, anovel procedure will be given. It will require establishing maximal regularityof the linearized, boundary feedback uniformly stable problem to handle the non-linearanalysis. This is joint work with Irena Lasiecka and Buddhika Priyasad.