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UID:news554@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20190114T101458
DTSTART;TZID=Europe/Zurich:20150924T161500
SUMMARY:Doktorkolloquium: Anna Bohun
DESCRIPTION:Several  physical phenomena arising in fluid dynamics and kinet
 ic equations can  be modeled by nonlinear transport PDE. Such quantities a
 re the vorticity  of a fluid\, or the density of a collection of particles
  advected by a  velocity field which is highly irregular. The theory of ch
 aracteristics  provides a link between this PDE and the ODE dX/dt=b(t\,X(t
 \,x))\, where  $b$ is the velocity field. Given a vector field with Sobole
 v or BV  regularity and bounded divergence\, the theory of DiPerna-Lions a
 nd  Ambrosio gives a good notion of solution to the ordinary differential 
  equation using the concept of regular Lagrangian flow. I will discuss  th
 e recent works with Crippa-Bouchut regarding Lagrangian flows  associated 
 to velocity fields with anisotropic regularity: those with  gradient given
  by the singular integral of an L1 function in some  directions\, and the 
 singular integral of a measure in others. This  answers positively the que
 stion of existence of Lagrangian solutions to  the Vlasov Poisson and Eule
 r equations with L1 data.
X-ALT-DESC: Several  physical phenomena arising in fluid dynamics and kinet
 ic equations can  be modeled by nonlinear transport PDE. Such quantities a
 re the vorticity  of a fluid\, or the density of a collection of particles
  advected by a  velocity field which is highly irregular. The theory of ch
 aracteristics  provides a link between this PDE and the ODE dX/dt=b(t\,X(t
 \,x))\, where  $b$ is the velocity field. Given a vector field with Sobole
 v or BV  regularity and bounded divergence\, the theory of DiPerna-Lions a
 nd  Ambrosio gives a good notion of solution to the ordinary differential 
  equation using the concept of regular Lagrangian flow. I will discuss  th
 e recent works with Crippa-Bouchut regarding Lagrangian flows  associated 
 to velocity fields with anisotropic regularity: those with  gradient given
  by the singular integral of an L<sup>1</sup> function in some  directions
 \, and the singular integral of a measure in others. This  answers positiv
 ely the question of existence of Lagrangian solutions to  the Vlasov Poiss
 on and Euler equations with L<sup>1</sup> data.
DTEND;TZID=Europe/Zurich:20150924T171500
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