# Infinite energy solutions to the Navier-Stokes equations in the half-space and applications

## TL;DR

This paper introduces recent advances in understanding the existence of solutions to the Navier-Stokes equations in a half-space, focusing on mild and weak solutions and their behavior near potential singularities.

## Contribution

It summarizes key results from two papers on mild and local energy weak solutions to Navier-Stokes in half-space, highlighting concentration phenomena near singularities.

## Key findings

- Existence of mild solutions in half-space
- Existence of local energy weak solutions
- Concentration of (sub)critical norms near singularities

## Abstract

This short note serves as an introduction to the papers arXiv:1711.01651 and arXiv:1711.04486 by Maekawa, Miura and Prange. These two works deal with the existence of mild solutions on the one hand and local energy weak solutions on the other hand to the Navier-Stokes equations in the half-space $\R^3_+$. We emphasize a concentration result for (sub)critical norms near a potential singularity. The contents of these notes were presented during the X-EDP seminar at IH\'ES in October 2017.