Invariance of the White Noise for the Ostrovsky equation

TL;DR

This paper constructs invariant measures for the Ostrovsky equation in the L^2 norm and proves local well-posedness in a specific Besov space, advancing understanding of the equation's mathematical properties.

Contribution

It introduces invariant measures for the Ostrovsky equation and establishes local well-posedness in a Besov space, which are novel results for this equation.

Findings

Invariant measures constructed for the Ostrovsky equation.

Local well-posedness proved in the Besov space ^s_{p,\u221e} for sp > -1.

Enhanced understanding of the equation's mathematical structure.

Abstract

In this paper, we construct invariant measures for the Ostrovsky equation associated with the norm $L^2$. On the other hand, we prove the local well- posedness in the besov space $\hat{b}^s_{p,\infty}$ for $sp >-1$.