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Generalized Burgers equation with rough transport noise

Author

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  • Hocquet, Antoine
  • Nilssen, Torstein
  • Stannat, Wilhelm

Abstract

We introduce a new technique for studying well posedness and energy estimates for evolution equations with a rough transport term. The technique is based on finding suitable space–time weight functions for the equations at hand. As an example we study the well posedness of the generalized viscous Burgers equation perturbed by a rough path transport noise.

Suggested Citation

  • Hocquet, Antoine & Nilssen, Torstein & Stannat, Wilhelm, 2020. "Generalized Burgers equation with rough transport noise," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2159-2184.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:2159-2184
    DOI: 10.1016/j.spa.2019.06.014
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    References listed on IDEAS

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    1. Diehl, Joscha & Oberhauser, Harald & Riedel, Sebastian, 2015. "A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 161-181.
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