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arXiv · 2501.17180

Improved quasi-invariance result for the periodic Benjamin-Ono-BBM equation

Justin Forlano
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Abstract

We extend recent results of Genovese-Luca-Tzvetkov (2022) regarding the quasi-invariance of Gaussian measures under the flow of the periodic Benjamin-Ono-BBM (BO-BBM) equation to the full range where BO-BBM is globally well-posed. The main difficulty is due to the critical nature of the dispersion which we overcome by combining the approach of Coe-Tolomeo (2024) with an iteration argument due to Forlano-Tolomeo (2024) to obtain long-time higher integrability bounds on the transported density.

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Justin Forlano. 2025-01-24. Improved quasi-invariance result for the periodic Benjamin-Ono-BBM equation. https://arxiv.org/abs/2501.17180

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