The paper proves conditional a priori bounds for the dynamic fractional Phi^4 equation on the three-torus for every subcritical exponent s in (3/4,1), assuming a suitable renormalised model exists.
Renormalised singular stochastic PDEs
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abstract
Extended decorations on naturally decorated trees were introduced in the work of Bruned, Hairer and Zambotti on algebraic renormalization of regularity structures to provide a convenient framework for the renormalization of systems of singular stochastic PDEs within that setting. This non-dynamical feature of the trees complicated the analysis of the dynamical counterpart of the renormalization process. We provide a new proof of the renormalized system by-passing the use of extended decorations and working for a large class of renormalization maps, with the BPHZ renormalization as a special case. The proof reveals important algebraic properties connected to preparation maps.
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math.AP 1years
2024 1verdicts
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A priori bounds for the dynamic fractional $\Phi^4$ model on $\mathbb{T}^3$ in the full subcritical regime
The paper proves conditional a priori bounds for the dynamic fractional Phi^4 equation on the three-torus for every subcritical exponent s in (3/4,1), assuming a suitable renormalised model exists.