Remarks on the stochastic transport equation with H\"{o}lder drift
Analysis of PDEs
2013-01-18 v1 Probability
Abstract
We consider a stochastic linear transport equation with a globally H\"{o}lder 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 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.
Keywords
Cite
@article{arxiv.1301.4012,
title = {Remarks on the stochastic transport equation with H\"{o}lder drift},
author = {Franco Flandoli and Massimiliano Gubinelli and Enrico Priola},
journal= {arXiv preprint arXiv:1301.4012},
year = {2013}
}
Comments
arXiv admin note: text overlap with arXiv:0809.1310