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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the structure of the shocks for the inviscid Burgers equation indimension 1 when the initial velocity is given by L\'evy noise, or equivalentlywhen the initial potential is a two-sided L\'evy process $\psi_0$. When$\psi_0$ is abrupt in the sense of Vigon or has bounded variation with$\limsup_{|h| \downarrow 0} h^{-2} \psi_0(h) = \infty$, we prove that the setof points with zero velocity is regenerative, and that in the latter case thisset is equal to the set of Lagrangian regular points, which is non-empty. When$\psi_0$ is abrupt we show that the shock structure is discrete. When $\psi_0$is eroded we show that there are no rarefaction intervals.

Structure of shocks in Burgers turbulence with L\'evy noise initial data