Generalized Burgers equation with rough transport noise
Antoine Hocquet, Torstein Nilssen, Wilhelm Stannat
TL;DR
This paper develops a novel method using space-time weights to analyze well-posedness and energy estimates for evolution equations with rough transport noise, demonstrated on a generalized Burgers equation.
Contribution
Introduces a new technique for handling rough transport noise in evolution equations via space-time weight functions, applied to a generalized Burgers equation.
Findings
Established well-posedness for the generalized Burgers equation with rough transport noise.
Developed energy estimates using the new weight function technique.
Provided a framework applicable to other equations with rough transport terms.
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.
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