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/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

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

Zendy Tools

Zendy Open

In this paper we consider the Cauchy problem on the angular cutoff Boltzmannequation near global Maxwillians for soft potentials either in the whole spaceor in the torus. We establish the existence of global unique mild solutions inthe space $L^p_vL^{\infty}_{T}L^{\infty}_{x}$ with polynomial velocity weightsfor suitably large $p\leq \infty$, whenever for the initial perturbation theweighted $L^p_vL^{\infty}_x$ norm can be arbitrarily large but the$L^1_xL^\infty_v$ norm and the defect mass, energy and entropy are sufficientlysmall. The proof is based on the local in time existence as well as the uniforma priori estimates via an interplay in $L^p_vL^{\infty}_{T}L^{\infty}_{x}$ and$L^{\infty}_{T}L^{\infty}_{x}L^1_v$.

Large amplitude solutions in $L^p_vL^\infty_TL^\infty_x$ to the Boltzmann equation for soft potentials