Forward Self-Similar Solutions of the Navier-Stokes Equations in the Half Space

TL;DR

This paper proves the existence of forward self-similar solutions to the 3D incompressible Navier-Stokes equations in the half space for large initial data, advancing understanding of fluid behavior near boundaries.

Contribution

It establishes the existence of such solutions for arbitrarily large initial data in the half space, a significant extension over previous results.

Findings

Existence of forward self-similar solutions for large initial data

Solutions valid in the 3D half space

Advances understanding of boundary-influenced fluid dynamics

Abstract

For the incompressible Navier-Stokes equations in the 3D half space, we show the existence of forward self-similar solutions for arbitrarily large self-similar initial data.