We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

A De Giorgi Argument for L∞ solution to the Boltzmann Equation without Angular Cutoff

Formal Metadata

Title
A De Giorgi Argument for L∞ solution to the Boltzmann Equation without Angular Cutoff
Title of Series
Number of Parts
19
Author
Contributors
License
CC Attribution - NonCommercial - NoDerivatives 2.0 Generic:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
Language

Content Metadata

Subject Area
Genre
Abstract
In this talk, after reviewing the work on global well-posednessof the Boltzmann equation without angular cutoff with algebraic decay tails,we will present a recent work on the global weighted L∞-solutions to the Boltzmann equation without angular cut off in the regime close to equilib-rium. A De Giorgi type argument, well developed for diffusion equations, iscrafted in this kinetic context with the help of the averaging lemma. Mores pecifically, we use a strong averaging lemma to obtain suitable Lp estimates for level-set functions. These estimates are crucial for constructing an ap-propriate energy functional to carry out the De Giorgi argument. Then weextend local solutions to global by using the spectral gap of the linearized Boltzmann operator with the convergence to the equilibrium state obtainedas a byproduct. This result fill in the gap of well-posedness theory for the Boltzmann equation without angular cut off in the L∞framework. The talk is based on the joint works with Ricardo Alonso, Yoshinori Morimoto and Weiran Sun.