Ordinary differential equations/Harmonic analysis
The Gelfand–Shilov smoothing effect for the radially symmetric homogeneous Landau equation with Shubin initial datum
Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 613-625.

In this paper, we study the Cauchy problem associated with the radially symmetric spatially homogeneous non-cutoff Landau equation with Maxwellian molecules, while the initial datum belongs to negative-index Shubin space, which can be characterized by spectral decomposition of the harmonic oscillators. Based on this spectral decomposition, we construct the weak solution with Shubin's class initial datum, and then we prove the uniqueness and the Gelfand–Shilov smoothing effect of the solution to this Cauchy problem.

Dans cet article, nous étudions le problème de Cauchy associé à l'équation de Landau spatialement homogène à symétrie radiale et sans troncature angulaire avec des molécules de Maxwell, tandis que la donnée initiale appartient à un espace de Shubin d'indice négatif, qui peut être caractérisé à partir de la décomposition spectrale de l'oscillateur harmonique quantique. En utilisant cette décomposition spectrale, nous construisons une solution faible avec une donnée initiale dans un espace de Shubin, puis nous prouvons l'unicité et un effet de régularisation de Gelfand–Shilov de la solution à ce problème de Cauchy.

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DOI: 10.1016/j.crma.2018.04.022
Li, Hao-Guang 1

1 School of Mathematics and Statistics, South-Central University for Nationalities, 430074, Wuhan, PR China
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Li, Hao-Guang. The Gelfand–Shilov smoothing effect for the radially symmetric homogeneous Landau equation with Shubin initial datum. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 613-625. doi : 10.1016/j.crma.2018.04.022. http://www.numdam.org/articles/10.1016/j.crma.2018.04.022/

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