On the parabolic and hyperbolic Liouville equations

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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.
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