Global well-posedness of the dynamical sine-Gordon model up to $6\pi$

Bjoern Bringmann; Sky Cao

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arXiv · 2410.15493

Global well-posedness of the dynamical sine-Gordon model up to $6\pi$

Bjoern Bringmann·Sky Cao

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Abstract

We prove the global well-posedness of the dynamical sine-Gordon model up to the third threshold, i.e., for parameters $\beta^2 < 6\pi$. The key novelty in our approach is the introduction of the so-called resonant equation, whose solution is entirely deterministic and completely captures the size of the solution to the dynamical sine-Gordon model. The probabilistic fluctuations in the dynamical sine-Gordon model are then controlled using uniform estimates for modified stochastic objects.

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Bjoern Bringmann, Sky Cao. 2024-10-20. Global well-posedness of the dynamical sine-Gordon model up to $6\pi$. https://arxiv.org/abs/2410.15493

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