Sharp Regularizing Effect of the Cauchy Problem for the Inhomogeneous Non-Cutoff Kac Equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918239214239744 |
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| author | Cai, Xinzhi Cao, Hongmei Xu, Chao-jiang |
| author_facet | Cai, Xinzhi Cao, Hongmei Xu, Chao-jiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp Regularizing Effect of the Cauchy Problem for the Inhomogeneous Non-Cutoff Kac Equation Cai, Xinzhi Cao, Hongmei Xu, Chao-jiang Analysis of PDEs 35B65, 35Q20, 35S30 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. |
| title | Sharp Regularizing Effect of the Cauchy Problem for the Inhomogeneous Non-Cutoff Kac Equation |
| topic | Analysis of PDEs 35B65, 35Q20, 35S30 |
| url | https://arxiv.org/abs/2512.08380 |