Global well-posedness of helicoidal Euler equations

TL;DR

This paper establishes the global existence and uniqueness of solutions for a special class of 3D incompressible Euler equations with helicoidal symmetry, addressing cases where the Beale-Kato-Majda criterion is not applicable.

Contribution

It proves global well-posedness for helicoidal Euler equations in critical spaces, a case not covered by existing criteria.

Findings

Global existence and uniqueness of solutions

Addresses cases beyond BKM criterion applicability

Focuses on helicoidal symmetry in Euler equations

Abstract

This paper deals with the global existence and uniqueness results for the three-dimensional incompressible Euler equations with a particular structure for initial data lying in critical spaces. In this case the BKM criterion is not known.