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arXiv · 1908.03944

On the parabolic and hyperbolic Liouville equations

Tadahiro Oh·Tristan Robert·Yuzhao Wang
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Abstract

We study the two-dimensional stochastic nonlinear heat equation (SNLH) and stochastic damped nonlinear wave equation (SdNLW) with an exponential nonlinearity $\lambda\beta e^{\beta u }$, forced by an additive space-time white noise. We prove local and global well-posedness of these equations, depending on the sign of $\lambda$ and the size of $\beta^2 > 0$, and invariance of the associated Gibbs measures. See the abstract of the paper for a more precise abstract. (Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here.)

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Tadahiro Oh, Tristan Robert, Yuzhao Wang. 2019-08-11. On the parabolic and hyperbolic Liouville equations. https://arxiv.org/abs/1908.03944

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