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DTSTART:20170326T030000
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DTSTART:20161030T020000
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DTSTAMP:20260428T211930Z
UID:58594cb3f3f1e377733543@ist.ac.at
DTSTART:20170110T094500
DTEND:20170110T104500
DESCRIPTION:Speaker: Maria Colombo\nAbstract: The transport equation descri
 bes the evolution of a distribution of particles moving along the flow (ch
 aracteristic curves) of a prescribed smooth vector field. An accurate desc
 ription of its solutions\, even when the smoothness assumption is dropped\
 , is motivated by several applications\, among which the study of kinetic 
 equations such as the Vlasov-Poisson system.\nGiven a vector field in R^d\
 , the classical Cauchy-Lipschitz theorem shows existence and uniqueness of
  its flow provided the vector field is sufficiently smooth\; this\, in tur
 n\, translates in existence and uniqueness results for the transport equat
 ion. In the last 30 years\, several efforts were made in order to lower th
 e regularity assumptions on the vector field\, like in the seminal paper b
 y Di Perna and Lions in 1989. They proved that Sobolev regularity for vect
 or fields\, with bounded divergence and a growth assumption\, is sufficien
 t to establish existence\, uniqueness and stability of a generalized notio
 n of flow\, consisting of a suitable selection among the trajectories of t
 he associated ODE. In the seminar I will go through this theory and presen
 t some recent results\, obtained in collaboration with Ambrosio and Figall
 i.
LOCATION:Raiffeisen Lecture Hall\, Central Building\, ISTA
ORGANIZER:pdelreal@ist.ac.at
SUMMARY:Maria Colombo: The structure of transport equations and the Vlasov-
 Poisson system
URL:https://talks-calendar.ista.ac.at/events/107
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