A solution theory for quasilinear singular SPDEs

M. Gerencser, M. Hairer, Communications on Pure and Applied Mathematics 72 (2019) 1983–2005.

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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
Volume
72
Issue
9
Page
1983-2005
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Gerencser M, Hairer M. A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics. 2019;72(9):1983-2005. doi:10.1002/cpa.21816
Gerencser, M., & Hairer, M. (2019). A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics, 72(9), 1983–2005. 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 72, no. 9 (2019): 1983–2005. 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, vol. 72, no. 9, pp. 1983–2005, 2019.
Gerencser M, Hairer M. 2019. A solution theory for quasilinear singular SPDEs. Communications on Pure and Applied Mathematics. 72(9), 1983–2005.
Gerencser, Mate, and Martin Hairer. “A Solution Theory for Quasilinear Singular SPDEs.” Communications on Pure and Applied Mathematics, vol. 72, no. 9, Wiley, 2019, pp. 1983–2005, doi:10.1002/cpa.21816.
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