Sharp Regularizing Effect of the Cauchy Problem for the Inhomogeneous Non-Cutoff Kac Equation
Analysis of PDEs
2025-12-10 v1
Abstract
In this work, we study the spatially inhomogeneous Kac equation with a non-cutoff cross section in a setting close to equilibrium. We prove that the solution to the Cauchy problem exhibits a sharp Gevrey-Gelfand-Shilov smoothing effect with an optimal radius. We employ a well-chosen exponential-type Fourier multiplier to establish the smoothing effect for position and velocity variables.
Cite
@article{arxiv.2512.08380,
title = {Sharp Regularizing Effect of the Cauchy Problem for the Inhomogeneous Non-Cutoff Kac Equation},
author = {Xinzhi Cai and Hongmei Cao and Chao-jiang Xu},
journal= {arXiv preprint arXiv:2512.08380},
year = {2025}
}
Comments
28 pages