dc.contributor.author Glass, Olivier dc.date.accessioned 2013-01-12T10:11:10Z dc.date.available 2013-01-12T10:11:10Z dc.date.issued 2012 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/10823 dc.language.iso en en dc.subject Control in Fluid Mechanics dc.subject Euler equation dc.subject Cauchy problem dc.subject.ddc 520 en dc.title Some Questions of Control in Fluid Mechanics dc.type Communication / Conférence dc.description.abstracten The goal of these lecture notes is to present some techniques of non-linear control of PDEs, in the context of fluid mechanics. We will consider the problem of controllability of two different models, namely the Euler equation for perfect incompressible fluids, and the one-dimensional isentropic Euler equation for compressible fluids. The standard techniques used to deal with the Cauchy problem for these two models are of rather different nature, despite the fact that the models are close. As we will see, this difference will also appear when constructing solutions of the controllability problem; however a common technique (or point of view) will be used in both cases. This technique, introduced by J.-M. Coron as the return method, is a way to exploit the nonlinearity of the equation for control purposes. Hence we will see its application in two rather different types of PDEs. The plan of these notes is the following. In a first part, we recall in a very basic way some types of questions that can be raised in PDE control (in a non-exhaustive way). In a second part, we expose results concerning the controllability of the incompressible Euler equation. In a third part, we show how the techniques used to prove the controllability of the incompressible Euler equation can be used to prove some other controllability properties for this equation, namely the so-called Lagrangian controllability. In a fourth and last part, we consider the controllability of the isentropic Euler equation. dc.identifier.citationpages 344 dc.relation.ispartoftitle Control of Partial Differential Equations dc.relation.ispartofeditor Fatiha Alabau-Boussouira, Roger Brockett, Olivier Glass, Jérôme Le Rousseau, Enrique Zuazua dc.relation.ispartofpublname Springer dc.relation.ispartofpublcity Berlin Heidelberg dc.relation.ispartofdate 2012 dc.relation.ispartofurl http://dx.doi.org/10.1007/978-3-642-27893-8 dc.subject.ddclabel Sciences connexes (physique, astrophysique) en dc.relation.ispartofisbn 978-3-642-27892-1 dc.relation.forthcoming non en dc.identifier.doi http://dx.doi.org/10.1007/978-3-642-27893-8_3 dc.description.ssrncandidate non dc.description.halcandidate oui dc.description.readership recherche dc.description.audience International dc.date.updated 2017-09-21T10:27:00Z
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