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It has been known for a while that a nonlinear equation driven by singularnoise must be interpreted in the re-normalized, or Wick, form. For thestochastic Burgers equation, Wick nonlinearity forces the solution to be ageneralized process no matter how regular the random perturbation is, whencethe curse. On the other hand, certain multiplicative random perturbations ofthe deterministic Burgers equation can only be interpreted in the Wick form,whence the cure. The analysis is based on the study of the coefficients of thechaos expansion of the solution at different stochastic scales.

Wick product in the stochastic Burgers equation: A curse or a cure?