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

2025/01/24 by Justin Forlano, Forlano, Justin · 1 citation
Mathematics · Physics and Astronomy · #35Q53 #76B15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Numerical methods for differential equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2501.17180

openalex publication_date 2025/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Quantitative quasi-invariance of Gaussian measures below the energy level for the 1D generalized nonlinear Schrödinger equation and application to global well-posedness

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