Analytic smoothing effect for a model of Kolmogorov-Prandtl type equations

In this note, we consider the Cauchy problem for a model of Kolmogorov-Prandtl type equations. For the small perturbation of a constant state, we prove that it admits a unique classical solution with the initial datum in Sobolev space, and it is analytic for any positive times.

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Journal
ArXiv.org
Published
2025-09-27
Primary Topic
X-ray Spectroscopy and Fluorescence Analysis
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article

Analytic smoothing effect for a model of Kolmogorov-Prandtl type equations

ArXiv.org
X-ray Spectroscopy and Fluorescence Analysis
article

Analytic smoothing effect for a model of Kolmogorov-Prandtl type equations

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Abstract

In this note, we consider the Cauchy problem for a model of Kolmogorov-Prandtl type equations. For the small perturbation of a constant state, we prove that it admits a unique classical solution with the initial datum in Sobolev space, and it is analytic for any positive times.

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Analytic smoothing effect for a model of Kolmogorov-Prandtl type equations · ArXiv.org (2025) | TGRS Research Map | TGRS