Sharp regularization effect for the non-cutoff Boltzmann equation with hard potentials

  • Jun-Ling Chen

    Wuhan University, Wuhan, China
  • Wei-Xi Li

    Wuhan University, Wuhan, China
  • Chao-Jiang Xu

    Nanjing University of Aeronautics and Astronautics, Nanjing, China
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Abstract

For the Maxwellian molecules or hard potentials case, we verify the smoothing effect for the spatially inhomogeneous Boltzmann equation without angular cutoff. Given initial data with low regularity, we prove solutions at any positive time are analytic for strong angular singularity, and in the Gevrey class with optimal index for mild angular singularity. To overcome the degeneracy in the spatial variable, a family of well-chosen vector fields with time-dependent coefficients will play a crucial role, and the sharp regularization effect of weak solutions relies on a quantitative estimate on directional derivatives in these vector fields.

Cite this article

Jun-Ling Chen, Wei-Xi Li, Chao-Jiang Xu, Sharp regularization effect for the non-cutoff Boltzmann equation with hard potentials. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024), published online first

DOI 10.4171/AIHPC/121