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SUMMARY:Flows of Irregular Vector Fields in Fluid Dynamics (3/6)
DTSTART:20240212T090000Z
DTEND:20240212T110000Z
DTSTAMP:20260418T173900Z
UID:indico-event-11318@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Maria Colombo (Ecole polytechnique fédérale de Lau
 sanne)\n\nAtttention : La première Leçon aura lieu à l'Ecole polytechni
 que\, Amphithéâtre Becquerel\, le 30 janvier à 15hRetrouvez toutes ces 
 informations sur le site de la Fondation Mathématique Jacques Hadamard :h
 ttps://www.fondation-hadamard.fr/en/events/advanced-courses/Abstract:Given
  a vector field in the euclidean space\, the classical Cauchy-Lipschitz th
 eorem shows existence and uniqueness of its flow provided the vector field
  is sufficiently smooth. The theorem looses its validity as soon as the ve
 ctor field is slightly less regular. However\, in 1989\, Di Perna and Lion
 s introduced a generalized notion of flow\, consisting of a suitable selec
 tion among the trajectories of the associated ODE\, and they showed existe
 nce\, uniqueness and stability for this notion of flow for much less regul
 ar vector fields.The course presents a modern view\, new results and open 
 problems in the context of flows of irregular vector fields.We develop\, i
 n this framework\, recent ideas and techniques such as quantitative regula
 rity estimates on the flow of Sobolev vector fields\, nonuniqueness of sol
 utions via convex integration\, similarity constructions\, mixing\, enhanc
 ed and anomalous dissipation.Such ideas have been proved useful to study n
 onlinear PDEs as well and we apply these results and techniques in the con
 text of the mathematical understanding of phenomena in fluid dynamics\, in
  particular for the Euler and Navier-Stokes equations and in relation to t
 he Kolmogorov theory of turbulence.\n\nhttps://indico.math.cnrs.fr/event/1
 1318/
LOCATION:Centre de conférences Marilyn et James Simons (IHES)
URL:https://indico.math.cnrs.fr/event/11318/
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