Author:
Alonso-Orán Diego,Bethencourt de León Aythami,Takao So
Abstract
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.
Funder
Schrodinger Scholarship Scheme
EPSRC
Spanish Ministry of Economy and Competitiveness
Severo Ochoa Programme for Centres of Excellence in R&D
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
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