A priori estimates for rough PDEs with application to rough conservation laws
Analysis of PDEs
2018-02-23 v4 Probability
Abstract
We introduce a general weak formulation for PDEs driven by rough paths, as well as a new strategy to prove well-posedness. Our procedure is based on a combination of fundamental a priori estimates with (rough) Gronwall-type arguments. In particular this approach does not rely on any sort of transformation formula (flow transformation, Feynman--Kac representation formula etc.) and is therefore rather flexible. As an application, we study conservation laws driven by rough paths establishing well--posedness for the corresponding kinetic formulation.
Keywords
Cite
@article{arxiv.1604.00437,
title = {A priori estimates for rough PDEs with application to rough conservation laws},
author = {Aurélien Deya and Massimiliano Gubinelli and Martina Hofmanová and Samy Tindel},
journal= {arXiv preprint arXiv:1604.00437},
year = {2018}
}
Comments
55 pages, substantially revised version