On the two-dimensional hyperbolic stochastic sine-Gordon equation
On the two-dimensional hyperbolic stochastic sine-Gordon equation
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DOI：
10.1007/s40072-020-00165-8
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发表时间：
2019-07
期刊：
影响因子：
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通讯作者：
Tadahiro Oh;T. Robert;Philippe Sosoe;Yuzhao Wang
中科院分区：
文献类型：
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作者：
Tadahiro Oh;T. Robert;Philippe Sosoe;Yuzhao Wang
研究了双曲背景下的二维随机sine-Gordon方程。特别地，通过对相应的虚高斯乘性混沌引入一个合适的含时重整化，我们证明了SSG对于非线性中的任意参数值的局部适定性。这与Hairer和Shen（Commun Math Phys 341（3）：933-989，2016）和Chandra等人（The dynamic sine-Gordon model in the full subcritical regime， 1808.02594 [math.PR]，2018），其中参数限制在亚临界范围内：。我们还提出了一个平凡的结果，未重整化的SSG。
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 foranyvalue of a parameterin 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, arXiv:1808.02594 [math.PR], 2018), where the parameter is restricted to the subcritical range:. We also present a triviality result for the unrenormalized SSG.