A solution theory for quasilinear singular SPDEs

M. Gerencser, M. Hairer, Communications on Pure and Applied Mathematics (2019).

Download
OA 333.65 KB

Journal Article | Epub ahead of print | English
Author
;
Department
Abstract
We give a construction allowing us to build local renormalized solutions to general quasilinear stochastic PDEs within the theory of regularity structures, thus greatly generalizing the recent results of [1, 5, 11]. Loosely speaking, our construction covers quasilinear variants of all classes of equations for which the general construction of [3, 4, 7] applies, including in particular one‐dimensional systems with KPZ‐type nonlinearities driven by space‐time white noise. In a less singular and more specific case, we furthermore show that the counterterms introduced by the renormalization procedure are given by local functionals of the solution. The main feature of our construction is that it allows exploitation of a number of existing results developed for the semilinear case, so that the number of additional arguments it requires is relatively small.
Publishing Year
Date Published
2019-02-08
Journal Title
Communications on Pure and Applied Mathematics
IST-REx-ID

Cite this

Gerencser M, Hairer M. A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics. 2019. doi:10.1002/cpa.21816
Gerencser, M., & Hairer, M. (2019). A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics. https://doi.org/10.1002/cpa.21816
Gerencser, Mate, and Martin Hairer. “A Solution Theory for Quasilinear Singular SPDEs.” Communications on Pure and Applied Mathematics, 2019. https://doi.org/10.1002/cpa.21816.
M. Gerencser and M. Hairer, “A solution theory for quasilinear singular SPDEs,” Communications on Pure and Applied Mathematics, 2019.
Gerencser M, Hairer M. 2019. A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics.
Gerencser, Mate, and Martin Hairer. “A Solution Theory for Quasilinear Singular SPDEs.” Communications on Pure and Applied Mathematics, Wiley, 2019, doi:10.1002/cpa.21816.
All files available under the following license(s):
Creative Commons License:
CC-BYCreative Commons Attribution 4.0 International Public License (CC-BY 4.0)
Main File(s)
Access Level
OA Open Access
Last Uploaded
2019-02-18T15:14:34Z


Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar