English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this article we study the Gevrey regularization effect for the spatiallyinhomogeneous Boltzmann equation without angular cutoff. This equation ispartially elliptic in the velocity direction and degenerates in the spatialvariable. We consider the nonlinear Cauchy problem for the fluctuation aroundthe Maxwellian distribution and prove that any solution with mild regularitywill become smooth in Gevrey class at positive time, with Gevrey indexdepending on the angular singularity. Our proof relies on the symbolic calculusfor the collision operator and the global subelliptic estimate for the Cauchyproblem of linearized Boltzmann operator.

Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off