On the two-dimensional hyperbolic stochastic sine-Gordon equation

被引：15

作者：

Oh, Tadahiro ^{[1
,2
]}

Robert, Tristan ^{[1
,2
,3
]}

Sosoe, Philippe ^{[4
]}

Wang, Yuzhao ^{[5
]}

机构：

[1] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland

[2] Maxwell Inst Math Sci, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland

[3] Univ Bielefeld, Fak Math, Postfach 10 01 31, D-33501 Bielefeld, Germany

[4] Cornell Univ, Dept Math, 584 Malott Hall, Ithaca, NY 14853 USA

[5] Univ Birmingham, Sch Math, Watson Bldg, Birmingham B15 2TT, W Midlands, England

来源：

STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS | 2021年 / 9卷 / 01期

基金：

欧洲研究理事会;

关键词：

Stochastic sine-Gordon equation; Sine-Gordon equation; Renormalization; White noise; Gaussian multiplicative chaos; STATISTICAL-MECHANICS; REGULARITY;

D O I：

10.1007/s40072-020-00165-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the two-dimensional stochastic sine-Gordon equation (SSG) in the hyperbolic setting. In particular, by introducing a suitable time-dependent renormalization for the relevant imaginary Gaussian multiplicative chaos, we prove local well-posedness of SSG for any value of a parameter beta 2>0in the nonlinearity. This exhibits sharp contrast with the parabolic case studied by Hairer and Shen (Commun Math Phys 341(3):933-989, 2016) and Chandra et al. (The dynamical sine-Gordon model in the full subcritical regime, [math.PR], 2018), where the parameter is restricted to the subcritical range: 0<beta 2<8 pi. We also present a triviality result for the unrenormalized SSG.

引用

页码：1 / 32

页数：32

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