Smoothing estimates for the kinetic transport equation at the critical regularity
Analysis of PDEs
2018-05-09 v1
Abstract
We prove smoothing estimates for velocity averages of the kinetic transport equation in hyperbolic Sobolev spaces at the critical regularity, leading to a complete characterisation of the allowable regularity exponents. Such estimates will be deduced from some mixed-norm estimates for the cone multiplier operator at a certain critical index. Our argument is not particular to the geometry of the cone and we illustrate this by establishing analogous estimates for the paraboloid.
Keywords
Cite
@article{arxiv.1709.04146,
title = {Smoothing estimates for the kinetic transport equation at the critical regularity},
author = {Neal Bez and Jayson Cunanan and Sanghyuk Lee},
journal= {arXiv preprint arXiv:1709.04146},
year = {2018}
}