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arXiv · 2512.08380

Sharp Regularizing Effect of the Cauchy Problem for the Inhomogeneous Non-Cutoff Kac Equation

Xinzhi Cai·Hongmei Cao·Chao-jiang Xu
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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.

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Xinzhi Cai, Hongmei Cao, Chao-jiang Xu. 2025-12-09. Sharp Regularizing Effect of the Cauchy Problem for the Inhomogeneous Non-Cutoff Kac Equation. https://arxiv.org/abs/2512.08380

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