Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation
Yoshinori Morimoto, Nicolas Lerner, Karel Pravda-Starov, Chao-Jiang Xu
TL;DR
This paper proves that solutions to the inhomogeneous non-cutoff Kac equation exhibit Gelfand-Shilov smoothing in velocity and Gevrey smoothing in position, indicating enhanced regularity properties of the model.
Contribution
It establishes new regularity results for the non-cutoff Kac equation, demonstrating Gelfand-Shilov and Gevrey smoothing effects in the inhomogeneous setting.
Findings
Gelfand-Shilov regularity in velocity variable
Gevrey regularity in position variable
Enhanced smoothing properties of the Kac equation
Abstract
We consider the spatially inhomogeneous non-cutoff Kac's model of the Boltzmann equation. We prove that the Cauchy problem for the fluctuation around the Maxwellian distribution enjoys Gelfand-Shilov regularizing properties with respect to the velocity variable and Gevrey regularizing properties with respect to the position variable.
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Taxonomy
TopicsGas Dynamics and Kinetic Theory · Numerical methods in inverse problems · Radiative Heat Transfer Studies