The defocusing quintic NLS on the real line has an invariant infinite-volume Gibbs measure for p between 3 and 5.
A simple construction of the sine-Gordon model via stochastic quantization
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abstract
We present a simple PDE construction of the sine-Gordon measure below the first threshold ($\be^2 < 4\pi$), in both the finite and infinite volume settings, by studying the corresponding parabolic sine-Gordon model. We also establish pathwise global well-posedness of the hyperbolic sine-Gordon model in finite volume for $\be^2 < 2\pi$.
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Invariant Gibbs measures for the one-dimensional quintic nonlinear Schr\"odinger equation in infinite volume
The defocusing quintic NLS on the real line has an invariant infinite-volume Gibbs measure for p between 3 and 5.