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arXiv · 1301.4012

Remarks on the stochastic transport equation with Hölder drift

Franco Flandoli·Massimiliano Gubinelli·Enrico Priola
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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.

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Franco Flandoli, Massimiliano Gubinelli, Enrico Priola. 2013-01-17. Remarks on the stochastic transport equation with Hölder drift. https://arxiv.org/abs/1301.4012

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