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SUMMARY:Stefano Bianchini (SISSA\, Trieste\, Italy)
DTSTART:20201027T093000Z
DTEND:20201027T103000Z
DTSTAMP:20260423T005730Z
UID:WOPARA/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WOPARA/11/">
 On the sticky particle solutions to the multi-dimensional pressureless Eul
 er equations</a>\nby Stefano Bianchini (SISSA\, Trieste\, Italy) as part o
 f Webinar on PDE and related areas\n\n\nAbstract\nAbstract:  In this talk 
 we consider the multi-dimensional pressureless Eulersystem and we tackle t
 he problem of existence and uniqueness of sticky particlesolutions for gen
 eral measure-type initial data.  Although explicit counterexam-ples to bot
 h existence and uniqueness are known\, the problem of whether onecan still
  find sticky particle solutions for a large set of data and of how one can
 select them was up to our knowledge still completely open.  In this talk w
 e provethat for a comeager set of initial data in the weak topology the pr
 essureless Eu-ler system admits a unique sticky particle solution given by
  a free flow wheretrajectories are disjoint straight lines.  Indeed\,  suc
 h an existence and unique-ness result holds for a broader class of solutio
 ns decreasing their kinetic energy\,which we call dissipative solutions\, 
 and which turns out to be the compact weakclosure of the classical sticky 
 particle solutions.  Therefore any scheme for whichthe energy is l.s.c.  a
 nd is dissipated will converge\, for a comeager set of data\,to our soluti
 on\, i.e.  the free flow\n
LOCATION:https://researchseminars.org/talk/WOPARA/11/
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