BibTex format
@unpublished{Chandra:2020,
author = {Chandra, A and Hairer, M and Shen, H},
title = {The dynamical sine-Gordon model in the full subcritical regime},
url = {http://arxiv.org/abs/1808.02594v1},
year = {2020}
}
Publications
Citation
RIS format (EndNote, RefMan)
TY - UNPB
AB - We prove that the dynamical sine-Gordon equation on the two dimensional torusintroduced in [HS16] is locally well-posed for the entire subcritical regime.At first glance this equation is far out of the scope of the local existencetheory available in the framework of regularity structures [Hai14, BHZ16, CH16,BCCH17] since it involves a non-polynomial nonlinearity and the solution isexpected to be a distribution (without any additional small parameter as in[FG17, HX18]). In [HS16] this was overcome by a change of variable, but the newequation that arises has a multiplicative dependence on highly non-Gaussiannoises which makes stochastic estimates highly non-trivial - as a result [HS16]was only able to treat part of the subcritical regime. Moreover, the cumulantsof these noises fall out of the scope of the later work [CH16]. In this work wesystematically leverage "charge" cancellations specific to this model andobtain stochastic estimates that allow us to cover the entire subcriticalregime.
AU - Chandra,A
AU - Hairer,M
AU - Shen,H
PY - 2020///
TI - The dynamical sine-Gordon model in the full subcritical regime
UR - http://arxiv.org/abs/1808.02594v1
ER -