The paper establishes local and global well-posedness for the 2D stochastic heat and damped wave equations with exponential nonlinearity in the ranges β²<1.37π (heat, any sign), β²<4π (heat, defocusing), and β²<0.86π (wave, defocusing), with invariance of the associated Gibbs measures.
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On the parabolic and hyperbolic Liouville equations
The paper establishes local and global well-posedness for the 2D stochastic heat and damped wave equations with exponential nonlinearity in the ranges β²<1.37π (heat, any sign), β²<4π (heat, defocusing), and β²<0.86π (wave, defocusing), with invariance of the associated Gibbs measures.