Aurélien Deya, Massimiliano Gubinelli, Martina Hofmanová and Samy Tindel
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.
Aurélien Deya, Massimiliano Gubinelli, Martina Hofmanová and Samy Tindel. A priori estimates for rough PDEs with application to rough conservation laws. Papers of Massimiliano Gubinelli, 2016, version 4. https://mgubi.org/papers/paper/rough-conservation-laws/
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Papers of Massimiliano Gubinelli: an OpenSheaf archive (format 0.1, a draft); this page is generated by opensheaf-py from the archive.