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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.

Xu , Chaojiang and Xu , Yan. (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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