Commutator method for averaging lemmas

Abstract

We introduce a commutator method with multipliers to prove averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations.This method requires only elementary techniques in Fourier analysis and shows a new range of assumptions that are sufficient for the velocity average to be in L 2 ([0, T ], H 1/2x ).This result not only shows an interesting connection between averaging lemmas and local smoothing property of dispersive equations, but also provide a direct proof for the regularizing effect for the measurevalued solutions of scalar conservation laws in space dimension one.

Locations

• Analysis & PDE - View
• arXiv (Cornell University) - View - PDF