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 [11,14] from d=3 to the entire subcritical regime.
Local well-posedness of subcritical non-linear heat equations with Gaussian initial data / Chevyrev, Ilya; Mirsajjadi, Hora. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 289:12(2025). [10.1016/j.jfa.2025.111160]
Local well-posedness of subcritical non-linear heat equations with Gaussian initial data
Chevyrev, Ilya;
2025-01-01
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 [11,14] from d=3 to the entire subcritical regime.File in questo prodotto:
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