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

· 2016 · math.AP · arXiv 1604.00437

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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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math.PR 1

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2019 1

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  • Dynamics of Stochastic Reaction-Diffusion Equations math.PR · 2019-08-24 · conditional · none · ref 58 · internal anchor

    This survey maps solution theory and dynamics of stochastic reaction-diffusion equations, reporting known results rather than proving new ones.