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.
Bony, Calcul symbolique et propagation des singularit´ es pour les ´ equations aux d´ eriv´ ees partielles non lin´ eaires,Ann
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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.