Well-posedness of the 2D Euler equations when velocity grows at infinity

TL;DR

This paper proves the uniqueness and finite-time existence of solutions to the 2D Euler equations with velocity fields that grow slower than the square root of the distance, ensuring global existence and stability.

Contribution

It establishes global existence and uniqueness of solutions for 2D Euler equations with specific velocity growth conditions, extending previous results.

Findings

Proved uniqueness of solutions with bounded vorticity.

Established finite-time existence for velocities growing slower than sqrt(distance).

Demonstrated continuous dependence on initial data.

Abstract

We prove the uniqueness and finite-time existence of bounded-vorticity solutions to the 2D Euler equations having velocity growing slower than the square root of the distance from the origin, obtaining global existence for more slowly growing velocity fields. We also establish continuous dependence on initial data.