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

Ilya Chevyrev; Hora Mirsajjadi

doi:10.1016/j.jfa.2025.111160

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arXiv · 2410.11638

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

Ilya Chevyrev·Hora Mirsajjadi

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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.

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Ilya Chevyrev, Hora Mirsajjadi. 2024-10-15. Local well-posedness of subcritical non-linear heat equations with Gaussian initial data. https://doi.org/10.1016/j.jfa.2025.111160

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