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SUMMARY:The solution of the Gevrey smoothing conjecture for the fully nonl
 inear homogeneous Boltzmann equation for Maxwellian molecules - Tobias Rie
 d (Karlsruhe Institute of Technology)
DTSTART:20160302T160000Z
DTEND:20160302T170000Z
UID:TALK64439@talks.cam.ac.uk
CONTACT:Mr Simone Parisotto
DESCRIPTION:While under the so called Grad cutoff assumption the homogeneo
 us Boltzmann equation is known to propagate smoothness and singularities\,
  it has long been suspected that the non-cutoff Boltzmann operator has sim
 ilar coercivity properties as a fractional Laplace operator. This has led 
 to the hope that the homogenous Boltzmann equation enjoys similar smoothin
 g properties as the heat equation with a fractional Laplacian.\nWe prove t
 hat any weak solution of the fully nonlinear non-cutoff homogenous Boltzma
 nn equation (for Maxwellian molecules) with initial datum f<sub>0</sub> wi
 th finite mass\, energy and entropy\, f<sub>0</sub>\\in L<sup>1</sup><sub>
 2</sub>(R<sup>d</sup>) \\cap LlogL(R<sup>d</sup>)\, immediately becomes Ge
 vrey regular for strictly positive times\, i.e. it gains infinitely many d
 erivatives and even (partial) analyticity.\nThis is achieved by an inducti
 ve procedure based on very precise estimates of nonlinear\, nonlocal commu
 tators of the Boltzmann operator with suitable test functions involving ex
 ponentially growing Fourier multipliers.\n(Joint work with Jean-Marie Barb
 aroux\, Dirk Hundertmark\, and Semjon Vugalter)
LOCATION:MR14\, Centre for Mathematical Sciences
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