Trapping regions and an ODE-type proof of the existence and uniqueness theorem for Navier-Stokes equations with periodic boundary conditions on the plane

TL;DR

This paper presents a novel proof of the existence and uniqueness of solutions to the Navier-Stokes equations with periodic boundary conditions on the plane, utilizing ODE methods and trapping regions.

Contribution

It introduces a new ODE-based proof approach for Navier-Stokes solutions, building on trapping regions by Mattingly and Sinai.

Findings

Proof of existence and uniqueness established

Method provides an alternative to traditional PDE approaches

Utilizes trapping regions to analyze solution behavior

Abstract

Using ODE-methods and trapping regions derived by Mattingly and Sinai we give a new proof of the existence and uniqueness of solutions to Navier-Stokes equations with periodic boundary conditions on the plane.