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Subcritical non-linear heat equations via spectral gap

Chevyrev, Ilya et al.
arXiv (All) · Papers
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analysis-of-pdesprobability
We establish local well-posedness for a class of non-linear heat equations on the torus $\mathbb{T}^n$ whose highest order non-linearities have scaling-critical dimension $-1/k, \, k\in \mathbb{N}$, when the initial condition is a random field satisfying a spectral gap inequality involving a suitabl
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