On the invariant measures for the Ostrovsky equation

TL;DR

This paper constructs invariant measures for the Ostrovsky equation linked to conservation laws and proves local well-posedness for initial data in certain Sobolev spaces.

Contribution

It introduces invariant measures for the Ostrovsky equation and establishes local well-posedness in periodic Sobolev spaces, advancing understanding of its mathematical properties.

Findings

Invariant measures associated with conservation laws are constructed.

Local well-posedness is proven for initial data in H^s with s > -1/2.

The results contribute to the mathematical theory of the Ostrovsky equation.

Abstract

In this paper, we construct invariant measures for the Ostrovsky equation associated with conservation laws. On the other hand, we prove the local well- posedness of the initial value problem for the periodic Ostrovsky equation with initial data in $H^{s}(\mathbb{T})$ for $s>-1/2$.