On the parabolic and hyperbolic Liouville equations

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.)

70 pages. To appear in Comm. Math. Phys. Minor typos corrected

References in corpus (3)

• Probabilistic local well-posedness of the cubic nonlinear wave equation in negative Sobolev spaces
• Focusing ${\Phi }_3^4$-model with a Hartree-type nonlinearity
• Stochastic Ricci Flow on Compact Surfaces

Cited by in corpus (4)

• Stochastic Ricci Flow on Compact Surfaces
• Stochastic quantization of Liouville conformal field theory
• Comparing the stochastic nonlinear wave and heat equations: a case study
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