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arXiv · 2606.12183

On the almost sure growth of Hölder norms for the 1d periodic fractional BBM equation

Pablo Merino
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Abstract

We present almost sure polynomial bounds for Hölder norms of solutions of the 1d periodic fractional Benjamin-Bona-Mahony (BBM) equation. Namely, we apply quantitative quasi-invariance of certain Gaussian measures with energy cutoff using the strategy from Tzvetkov (2015) and the globalization argument from Bourgain (1994) in order to extend, almost surely, the $L^2$-based deterministic control to the $L^{\infty}$-based setting.

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Pablo Merino. 2026-06-10. On the almost sure growth of Hölder norms for the 1d periodic fractional BBM equation. https://arxiv.org/abs/2606.12183

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