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 languageEnglish
Number of pages32
JournalStochastics and Partial Differential Equations: Analysis and Computations
Early online date5 Feb 2020
DOIs
Publication statusE-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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