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

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 multiplicative Gaussian 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.
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Cited literature [45 references]

https://hal.archives-ouvertes.fr/hal-02434797
Contributor : Tristan Robert <>
Submitted on : Thursday, September 17, 2020 - 5:08:07 PM
Last modification on : Monday, January 25, 2021 - 2:36:02 PM
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Tadahiro Oh, Tristan Robert, Philippe Sosoe, Yuzhao Wang. On the two-dimensional hyperbolic stochastic sine-Gordon equation. Stochastics and Partial Differential Equations: Analysis and Computations, Springer US, 2020, ⟨10.1007/s40072-020-00165-8⟩. ⟨hal-02434797⟩

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