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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the sticky particle solutions to the pressurele
 ss Euler system in general dimension - Sara Daneri
  (Gran Sasso Science Institute\, L'Aquila)
DTSTART;TZID=Europe/London:20220214T133000
DTEND;TZID=Europe/London:20220214T143000
UID:TALK167324AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/167324
DESCRIPTION:In this talk we consider the pressureless Euler sy
 stem in dimension greater than or equal to two. Se
 veral works have been devoted to the search of sol
 utions which satisfy the following adhesion or sti
 cky particle principle: if two particles of the fl
 uid do not interact\, then they move freely keepin
 g constant velocity\, otherwise they join with vel
 ocity given by the balance of momentum. For initia
 l data given by a finite number of particles point
 ing each in a given direction\, in general dimensi
 on\, it is easy to show that a global sticky parti
 cle solution always exists and is unique. In dimen
 sion one\, sticky particle solutions have been pro
 ved to exist and be unique.&nbsp\; In dimension gr
 eater or equal than two\, it was shown that as soo
 n as the initial data is not concentrated on a fin
 ite number of particles\, it might lead to non-exi
 stence or non-uniqueness of sticky particle soluti
 ons.\nIn collaboration with S. Bianchini\,&nbsp\; 
 we show that&nbsp\; even though the sticky particl
 e solutions are not well-posed for every measure-t
 ype initial data\, there exists a comeager set of 
 initial data in the weak topology giving rise to a
  unique sticky particle solution. Moreover\, for a
 ny of these initial data the sticky particle &nbsp
 \;solution is unique also in the larger class of d
 issipative solutions (where trajectories are allow
 ed to cross) and is given by a trivial free flow c
 oncentrated on trajectories which do not intersect
 . In particular for such initial data there is onl
 y one dissipative solution and its dissipation is 
 equal to zero. Thus\, for a comeager set of initia
 l data the problem of finding sticky particle solu
 tions is well-posed\, but the dynamics that one &n
 bsp\;sees is trivial. Our notion of dissipative so
 lution is lagrangian and therefore general enough 
 to include weak and measure-valued solutions.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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