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Volume 37, Issue 1
Analytic Smoothing Effect of the Time Variable for the Spatially Homogeneous Landau Equation

Chaojiang Xu & Yan Xu

DOI: 10.4208/jpde.v37.n1.5

J. Part. Diff. Eq., 37 (2024), pp. 88-103.

Published online: 2024-02

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  • Abstract

In this work, we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework. We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an $L^2$ initial datum for positive time. So that the smoothing effect of the Cauchy problem for the spatially homogeneous Landau equation with hard potentials is exactly same as heat equation.

  • Keywords

Spatially homogeneous Landau equation, analytic smoothing effect, hard potentials.

  • AMS Subject Headings

35B65, 76P05, 82C40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-37-88, author = {Xu , Chaojiang and Xu , Yan}, title = {Analytic Smoothing Effect of the Time Variable for the Spatially Homogeneous Landau Equation}, journal = {Journal of Partial Differential Equations}, year = {2024}, volume = {37}, number = {1}, pages = {88--103}, abstract = {

In this work, we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework. We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an $L^2$ initial datum for positive time. So that the smoothing effect of the Cauchy problem for the spatially homogeneous Landau equation with hard potentials is exactly same as heat equation.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v37.n1.5}, url = {http://global-sci.org/intro/article_detail/jpde/22907.html} }
TY - JOUR T1 - Analytic Smoothing Effect of the Time Variable for the Spatially Homogeneous Landau Equation AU - Xu , Chaojiang AU - Xu , Yan JO - Journal of Partial Differential Equations VL - 1 SP - 88 EP - 103 PY - 2024 DA - 2024/02 SN - 37 DO - http://doi.org/10.4208/jpde.v37.n1.5 UR - https://global-sci.org/intro/article_detail/jpde/22907.html KW - Spatially homogeneous Landau equation, analytic smoothing effect, hard potentials. AB -

In this work, we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework. We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an $L^2$ initial datum for positive time. So that the smoothing effect of the Cauchy problem for the spatially homogeneous Landau equation with hard potentials is exactly same as heat equation.

Chaojiang Xu & Yan Xu. (2024). Analytic Smoothing Effect of the Time Variable for the Spatially Homogeneous Landau Equation. Journal of Partial Differential Equations. 37 (1). 88-103. doi:10.4208/jpde.v37.n1.5
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