# Quasi-linear singular stochastic PDE

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Felix Otto, Max Planck Institute Leipzig

We are interested in parabolic differential equations $\partial_tu-a(u)\partial_x^2u=\xi$ with random forcing $\xi$, and non-linearity in the leading order term. For a forcing that is only in the (parabolic) Hölder space $C^\alpha$ with $\alpha<1$, this equation requires a renormalization. This can be done within Gubinelli's framework of controlled rough paths and, down to any $\alpha>0$, in Hairer's framework of regularity structures.