Remarks on the stochastic transport equation with Hölder drift

2013/01/17 by Flandoli, Franco, Gubinelli, Massimiliano, Priola, Enrico
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1301.4012

Abstract

We consider a stochastic linear transport equation with a globally Hölder continuous and bounded vector field. Opposite to what happens in the deterministic case where shocks may appear, we show that the unique solution starting with a C¹-initial condition remains of class C¹ in space. We also improve some results of Flandoli-Gubinelli-Priola (2009) about well-posedness. Moreover, we prove a stability property for the solution with respect to the initial datum.

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