Remarks on the stochastic transport equation with Hölder drift

Franco Flandoli, Massimiliano Gubinelli and Enrico Priola

First issued 17 January 2013 · PDF

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 C^1-initial condition remains of class $C^{1}$ 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.

Versions

1. Version 1 (arXiv v1) current
   17 January 2013
   arXiv comments: arXiv admin note: text overlap with arXiv:0809.1310
   PDF · LaTeX source · files and digests · arXiv:1301.4012

Cite

Franco Flandoli, Massimiliano Gubinelli and Enrico Priola. Remarks on the stochastic transport equation with Hölder drift. Papers of Massimiliano Gubinelli, 2013, version 1. https://mgubi.org/papers/paper/stochastic-transport-holder/

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