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Volume 40, Issue 1
A Remark about Time-Analyticity of the Linear Landau Equation with Soft Potential

Chaojiang Xu & Yan Xu

DOI: 10.4208/ata.OA-2022-0029

Anal. Theory Appl., 40 (2024), pp. 22-37.

Published online: 2024-04

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  • Abstract

In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. 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 Cauchy problem for the linear spatially homogeneous Landau equation with soft potentials is similar to the heat equation.

  • Keywords

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

  • AMS Subject Headings

35B65, 76P05, 82C40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-40-22, author = {Xu , Chaojiang and Xu , Yan}, title = {A Remark about Time-Analyticity of the Linear Landau Equation with Soft Potential}, journal = {Analysis in Theory and Applications}, year = {2024}, volume = {40}, number = {1}, pages = {22--37}, abstract = {

In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. 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 Cauchy problem for the linear spatially homogeneous Landau equation with soft potentials is similar to the heat equation.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2022-0029}, url = {http://global-sci.org/intro/article_detail/ata/23018.html} }
TY - JOUR T1 - A Remark about Time-Analyticity of the Linear Landau Equation with Soft Potential AU - Xu , Chaojiang AU - Xu , Yan JO - Analysis in Theory and Applications VL - 1 SP - 22 EP - 37 PY - 2024 DA - 2024/04 SN - 40 DO - http://doi.org/10.4208/ata.OA-2022-0029 UR - https://global-sci.org/intro/article_detail/ata/23018.html KW - Spatially homogeneous Landau equation, analytic smoothing effect, soft potentials. AB -

In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. 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 Cauchy problem for the linear spatially homogeneous Landau equation with soft potentials is similar to the heat equation.

Xu , Chaojiang and Xu , Yan. (2024). A Remark about Time-Analyticity of the Linear Landau Equation with Soft Potential. Analysis in Theory and Applications. 40 (1). 22-37. doi:10.4208/ata.OA-2022-0029
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