A priori estimates for rough PDEs with application to rough conservation laws |
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| Authors: | Aurélien Deya Massimiliano Gubinelli Martina Hofmanová Samy Tindel |
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| Institution: | 1. Institut Elie Cartan, University of Lorraine B.P. 239, 54506 Vandoeuvre-lès-Nancy, Cedex, France;2. Hausdorff Center for Mathematics & Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany;3. Institute of Mathematics, Technical University Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany;4. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, United States |
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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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| Keywords: | 60H15 35R60 35L65 Rough paths Rough PDEs A priori estimates Scalar conservation laws |
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