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SUMMARY:Luis Silvestre (University of Chicago)
DTSTART:20210701T153000Z
DTEND:20210701T163000Z
DTSTAMP:20260423T040036Z
UID:SIAM-PDE/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIAM-PDE/12/
 ">Gaussian lower bounds for the Boltzmann equation without cut-off</a>\nby
  Luis Silvestre (University of Chicago) as part of Seminar In the Analysis
  and Methods of PDE (SIAM PDE)\n\n\nAbstract\nThe Boltzmann equation model
 s the evolution of densities of particles in a gas. Its global well posedn
 ess is a major open problem\, facing comparable difficulties as similar qu
 estions for equations in fluids. With current techniques\, we cannot rule 
 out the possibility of a spontaneous emergence of a singularity in the for
 m of infinite mass or energy density concentrating at some point in space.
  This work is part of a series of a priori estimates for the inhomogeneous
  non-cutoff Boltzmann equation that are conditional to bounds on macroscop
 ic quantities. We establish a Gaussian lower bound for solutions to the Bo
 ltzmann equation without cutoff\, in the case of hard and moderately soft 
 potentials\, with spatial periodic conditions\, and under the sole assumpt
 ion that hydrodynamic quantities (local mass\, local energy and local entr
 opy density) remain bounded. In the talk\, we will discuss how this lower 
 bound fits in the larger program of conditional estimates.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/12/
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