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The Gelfand-Shilov smoothing effect for the radially symmetric homogeneous Landau equation with Shubin initial datum. (L’effet de lissage de Gelfand-Shilov pour l’équation de Landau homogène à symétrie radiale, avec donnée initiale de Shubin.) (English. French summary) Zbl 1394.35066

Summary: 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.

MSC:

35B65 Smoothness and regularity of solutions to PDEs
35D30 Weak solutions to PDEs
35E15 Initial value problems for PDEs and systems of PDEs with constant coefficients
35B07 Axially symmetric solutions to PDEs
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