| Abstract: | We will discuss quasi-linear parabolic equations driven by an additive forcing, in the full sub-critical regime . Our arguments are inspired by Hairer's regularity structures, however we work with a more parsimonious model indexed by multi-indices rather than trees. This allows us to capture additional symmetries which play a crucial role in our analysis. Assuming bounds on this model, which is modified in agreement with the concept of algebraic renormalization, we prove local a priori estimates on solutions to the quasi-linear equations modified by the corresponding counter terms. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber. |
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