Pith. sign in

REVIEW 2 cited by

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1808.07821 v3 pith:BQL6SDKM submitted 2018-08-23 math.AP

Diego Alonso-Orán , Aythami Bethencourt de León , So Takao This is my paper · ORCID
classification math.AP
keywords stochasticequationexistencesmoothsolutionsburgerscaseformation
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

In this work, we examine the solution properties of the Burgers' equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation and then obtain a stochastic Rankine-Hugoniot condition that the shocks satisfy. Next, we establish the local existence and uniqueness of smooth solutions in the inviscid case and construct a blow-up criterion. Finally, in the viscous case, we prove global existence and uniqueness of smooth solutions.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Modelling the climate and weather of a 2D Lagrangian-averaged Euler-Boussinesq equation with transport noise

    math-ph 2019-09 conditional novelty 7.0 of 10

    Global well-posedness and closed fluctuation-statistics equations are proven for the Lagrangian-averaged SALT 2D Euler-Boussinesq system.

  2. Lagrangian averaged stochastic advection by Lie transport for fluids

    math-ph 2019-08 conditional novelty 5.0 of 10

    The paper formulates LA SALT stochastic fluid equations whose mean field satisfies a closed Lie-Laplacian Navier-Stokes equation, and establishes well-posedness and fluctuation variance dynamics.

Pith tools