Seminars & Colloquia Calendar
Clement Mouhot - Quantitative linear stability of charged collisional particles in a confining field
Date & time: Thursday, 09 July 2020 at 11:00AM - 12:00PM
MATHEMATICAL PHYSICS WEBINAR
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Clement Mouhot - University of Cambridge
Thursday, July 9, 11:00AM
"Quantitative linear stability of charged collisional particles in a confining field”
We report on recent joint results in which we develop quantitative methods for proving the existence of a spectral gap and estimating the gap, for hypocoercive kinetic equations that combine the local conservation laws of fluid mechanics and a confining potential force. The proofs involve a cascade of correctors and global commutator estimates, as well as new quantitative inequalities of Korn type. The latter extend to the case of the whole space with a potential force
the classical Korn inequality in a bounded domain of elasticity theory. These results are a step towards constructing global solutions near equilibrium to the full nonlinear Boltzmann equation for charged particles subject to a confining potential. This is a series of two joint works with K. Carrapatoso, J. Dolbeault, F. Hérau and S. Mischler.