Regularizing effects in a linear kinetic equation for cubic interactions (Q6635655)
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scientific article; zbMATH DE number 7941400
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regularizing effects in a linear kinetic equation for cubic interactions |
scientific article; zbMATH DE number 7941400 |
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Regularizing effects in a linear kinetic equation for cubic interactions (English)
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12 November 2024
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This article presents two new major results concerning the linearized kinetic equation for nonlinear waves satisfying the Schrödinger equation. The first result is established with the fundamental solution and the second result concerns the smoothing effects of the equation. The results show that, thanks to what the author found in [J. Funct. Anal. 282, No. 8, Article ID 109390, 87 p. (2022; Zbl 1491.35382)], an important singularity regularizes instantaneously, and solutions also satisfy certain weighted Hölder continuity that improves in time.
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Cauchy problem
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regularity of solutions
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Sobolev spaces
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derivative of logarithmic order
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