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 Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In [L. Liu and S. Jin, Multiscale Model. Simult., 16, 1085-1114, 2018], spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the stochastic Galerkin approximation for the Boltzmann equation with random inputs in the initial data and collision kernel for hard potentials and Maxwellian molecules under Grad's angular cutoff were established using the hypocoercive properties of the collisional kinetic model. One assumption for the random perturbation of the collision kernel is that the perturbation is in the order of the Knudsen number, which can be very small in the fluid dynamical regime. In this article, we remove this smallness assumption, and establish the same results but now for random perturbations of the collision kernel that can be of order one. The new analysis relies on the establishment of a spectral gap for the numerical collision operator.

kinetic and related models

Spectral convergence of the stochastic galerkin approximation to the boltzmann equation with multiple scales and large random perturbation in the collision kernel