# On the two-dimensional hyperbolic stochastic sine-Gordon equation

Tadahiro Oh, Tristan Robert, Philippe Sosoe, Yuzhao Wang

Research output: Contribution to journalArticlepeer-review

## Abstract

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 $\beta^2 > 0$ in the nonlinearity. This exhibits sharp contrast with the parabolic case studied by Hairer and Shen (2016) and Chandra, Hairer, and Shen (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.
Original language English 32 Stochastics and Partial Differential Equations: Analysis and Computations 5 Feb 2020 https://doi.org/10.1007/s40072-020-00165-8 E-pub ahead of print - 5 Feb 2020

## Keywords

• stochastic sine-Gordon equation
• sine-Gordon equation
• renormalization
• white noise
• Gaussian multiplicative chaos

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