High order paracontrolled calculus
Classical Analysis and ODEs
2019-10-11 v5 Analysis of PDEs
Probability
Abstract
We develop in this work a general version of paracontrolled calculus that allows to treat analytically within this paradigm some singular partial differential equations with the same efficiency as regularity structures. This work deals with the analytic side of the story and offers a toolkit for the study of such equations, under the form of a number of continuity results for some operators. We illustrate the efficiency of this elementary approach on the examples of the 3-dimensional generalised parabolic Anderson model equation and the generalised KPZ equation driven by a (1+1)-dimensional space/time white noise.
Keywords
Cite
@article{arxiv.1609.06966,
title = {High order paracontrolled calculus},
author = {I. Bailleul and F. Bernicot},
journal= {arXiv preprint arXiv:1609.06966},
year = {2019}
}
Comments
v5, 67 pages. Refined correctors introduced, and an improved continuity result for the merging operator proved. Final version