Invariant Gibbs dynamics for the dynamical sine-Gordon model
Invariant Gibbs dynamics for the dynamical sine-Gordon model
复制标题
动态正弦戈登模型的不变吉布斯动力学
DOI：
10.1017/prm.2020.68
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
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
本文研究了二维环面上的双曲型随机阻尼sine-Gordon方程（SdSG），其中参数β2 > 0，以及相应的Gibbs动力学.在引入合适的重正化之后，我们首先通过Barashkov-Gubinelli（2018）的变分方法构造0 < β2 < 4π范围内的吉布斯测度。然后我们证明了在0 < β2 < 2π范围内，Gibbs测度在双曲SdSG动力学下的几乎必然的整体适定性和不变性.我们构造的Gibbs测度在0 < β2 < 4π的范围内也得到了抛物sine-Gordon模型的Gibbs测度的几乎必然的整体适定性和不变性.
In this note, we study the hyperbolic stochastic damped sine-Gordon equation (SdSG), with a parameter β2 > 0, and its associated Gibbs dynamics on the two-dimensional torus. After introducing a suitable renormalization, we first construct the Gibbs measure in the range 0 < β2 < 4π via the variational approach due to Barashkov-Gubinelli (2018). We then prove almost sure global well-posedness and invariance of the Gibbs measure under the hyperbolic SdSG dynamics in the range 0 < β2 < 2π. Our construction of the Gibbs measure also yields almost sure global well-posedness and invariance of the Gibbs measure for the parabolic sine-Gordon model in the range 0 < β2 < 4π.