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math.AP2019
Well-posedness by noise for linear advection of -forms
Aythami Bethencourt de Leon, So Takao
In this work, we extend existing well-posedness by noise results for the stochastic transport and continuity equations by treating them as special cases of the linear advection equ…
math.AP2018
The Burgers' equation with stochastic transport: shock formation, local and global existence of smooth solutions
Diego Alonso-Orán, Aythami Bethencourt de León, So Takao
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 a…