Invariant measures and long time behaviour for the Benjamin-Ono equation III

TL;DR

This paper advances the understanding of the Benjamin-Ono equation by constructing an infinite sequence of Gaussian-type invariant measures linked to its conservation laws, enhancing the analysis of its long-term dynamics.

Contribution

It completes a series of works by explicitly constructing invariant measures for the Benjamin-Ono equation, a significant step in understanding its long-term behavior.

Findings

Constructed an infinite sequence of invariant measures.

Linked invariant measures to conservation laws.

Enhanced understanding of long-time dynamics.

Abstract

We complete the program developed in our previous works aiming to construct an infinite sequence of invariant measures of gaussian type associated with the conservation laws of the Benjamin-Ono equation.