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arXiv · 1604.00437

A priori estimates for rough PDEs with application to rough conservation laws

Aurélien Deya·Massimiliano Gubinelli·Martina Hofmanová·Samy Tindel
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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.

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Aurélien Deya, Massimiliano Gubinelli, Martina Hofmanová, Samy Tindel. 2016-04-01. A priori estimates for rough PDEs with application to rough conservation laws. https://arxiv.org/abs/1604.00437

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