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CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:The solution of the Gevrey smoothing conjecture fo
r the fully nonlinear homogeneous Boltzmann equati
on for Maxwellian molecules - Tobias Ried (Karlsru
he Institute of Technology)
DTSTART;TZID=Europe/London:20160302T160000
DTEND;TZID=Europe/London:20160302T170000
UID:TALK64439AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/64439
DESCRIPTION:While under the so called Grad cutoff assumption t
he homogeneous Boltzmann equation is known to prop
agate smoothness and singularities\, it has long b
een suspected that the non-cutoff Boltzmann operat
or has similar coercivity properties as a fraction
al Laplace operator. This has led to the hope that
the homogenous Boltzmann equation enjoys similar
smoothing properties as the heat equation with a f
ractional Laplacian.\nWe prove that any weak solut
ion of the fully nonlinear non-cutoff homogenous B
oltzmann equation (for Maxwellian molecules) with
initial datum f0 with finite mass\, ene
rgy and entropy\, f0\\in L1<
sub>2(Rd) \\cap LlogL(Rd)\, immediately becomes Gevrey regular for stric
tly positive times\, i.e. it gains infinitely many
derivatives and even (partial) analyticity.\nThis
is achieved by an inductive procedure based on ve
ry precise estimates of nonlinear\, nonlocal commu
tators of the Boltzmann operator with suitable tes
t functions involving exponentially growing Fourie
r multipliers.\n(Joint work with Jean-Marie Barbar
oux\, Dirk Hundertmark\, and Semjon Vugalter)
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:Mr Simone Parisotto
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