The role of spectral anisotropy in the resolution of the three-dimensional Navier-Stokes equations

TL;DR

This paper investigates how spectral anisotropy in initial data influences the global existence and uniqueness of solutions to the 3D Navier-Stokes equations, introducing new classes of initial data with anisotropic frequency distributions.

Contribution

It introduces new classes of anisotropic initial data that guarantee global solutions despite large norms, expanding understanding of initial conditions for Navier-Stokes solutions.

Findings

Global solutions are achieved with anisotropic initial data.

Certain anisotropic distributions allow fixed-point local solutions.

New classes of initial data extend previous results.

Abstract

We present different classes of initial data to the three-dimensional, incompressible Navier-Stokes equations, which generate a global in time, unique solution though they may be arbitrarily large in the end-point function space in which a fixed-point argument may be used to solve the equation locally in time. The main feature of these initial data is an anisotropic distribution of their frequencies. One of those classes is taken from previous papers by two of the authors and collaborators, and another one is new.