Local well-posedness of subcritical non-linear heat equations with Gaussian initial data

Abstract

We show that any non-linear heat equation with scaling critical dimension $-1$ is locally well-posed when its initial condition is taken as the Gaussian free field in fractional dimension $d<4$. Our results in particular extend the well-posedness results of arXiv:2111.10652, arXiv:2201.03487 from $d=3$ to the entire subcritical regime.

arXiv comment45 pages, 3 Figures. Minor revisions. Accepted version in Journal of Functional Analysis

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• Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs