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 work, we examine the solution properties of the Burgers' equationwith stochastic transport. First, we prove results on the formation of shocksin the stochastic equation and then obtain a stochastic Rankine-Hugoniotcondition that the shocks satisfy. Next, we establish the local existence anduniqueness of smooth solutions in the inviscid case and construct a blow-upcriterion. Finally, in the viscous case, we prove global existence anduniqueness of smooth solutions.

The Burgers' equation with stochastic transport: shock formation, local and global existence of smooth solutions