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

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arxiv 1604.00437 v4 pith:SC25JLJ3 submitted 2016-04-01 math.AP math.PR

Aurélien Deya , Massimiliano Gubinelli , Martina Hofmanová , Samy Tindel This is my paper · ORCID
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keywords roughapplicationconservationdrivenestimatesformulaformulationlaws
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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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    This survey maps solution theory and dynamics of stochastic reaction-diffusion equations, reporting known results rather than proving new ones.

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