Short and long time behavior of the Fokker-Planck equation in a confining potential and applications

By Frédéric Hérau. 2005

146 citations recorded by the source corpus.

We consider the linear Fokker-Planck equation in a confining po- tential in space dimension d ≥ 3. Using spectral methods, we prove bounds on the derivatives of the solution for short and long time, and give some applica- tions.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4d8273da55513be9e5b7f59a5a8fb0d8b2315f2f

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In Applied Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

Exponential Stability of Slowly Decaying Solutions to the Kinetic-Fokker-Planck Equation (2014, methodology): “We only sketch the proof which is similar to the arguments developed in [15], see also [24, A.”
Hypocoercivity (2006, unknown): “Research in the area of hypocoercivity is currently developing fast thanks to the efforts of several other researchers such as Thierry Gallay, Frédéric Hérau, Clément Mouhot, and others.”
Spectral analysis of semigroups and growth-fragmentation equations (2013, background): “We refer the interested reader to [104] for a pedagogical introduction as well as to [56, 53, 88, 54, 55, 105, 29, 28] for some of the original articles.”
Enhanced Dissipation, Hypoellipticity, and Anomalous Small Noise Inviscid Limits in Shear Flows (2015, background): “[17,18,25,26] and the references therein or the text [47] for an overview of the basic ideas and a general study of hypocoercivity applied to linear operators in Hörmander form.”
Hypocoercive Diffusion Operators (2006, background): “I started to work on this approach while struggling to understand the results of Frédéric Hérau and Francis Nier [19], without resorting to the technical hypoelliptic machinery used in their work.”