Gluing non-unique Navier-Stokes solutions

TL;DR

This paper constructs non-unique solutions to the Navier-Stokes equations in bounded domains using gluing techniques, highlighting the local and robust nature of non-uniqueness in fluid dynamics.

Contribution

It introduces a novel gluing method to explicitly construct non-unique Leray solutions for forced Navier-Stokes equations in bounded domains.

Findings

Demonstrates non-uniqueness of solutions in bounded domains

Shows robustness and locality of non-uniqueness phenomena

Provides explicit construction of non-unique solutions

Abstract

We construct non-unique Leray solutions of the forced Navier-Stokes equations in bounded domains via gluing methods. This demonstrates a certain locality and robustness of the non-uniqueness discovered by the authors in [1].