For the quadratic stochastic nonlinear wave and heat equations on the two-dimensional torus, standard Da Prato-Debussche solution theory fails at noise roughness alpha = 1/2 (wave) and alpha = 1 (heat), before the scaling-critical values 3/4 and 2.
On the parabolic and hyperbolic Liouville equations
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.)
fields
math.AP 1years
2019 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Comparing the stochastic nonlinear wave and heat equations: a case study
For the quadratic stochastic nonlinear wave and heat equations on the two-dimensional torus, standard Da Prato-Debussche solution theory fails at noise roughness alpha = 1/2 (wave) and alpha = 1 (heat), before the scaling-critical values 3/4 and 2.