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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. \; 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\, \;
we show that \; 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
\;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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