# A weighted setting for the stationary Navier Stokes equations under singular forcing

## TL;DR

This paper establishes the existence of solutions to the 2D stationary Navier-Stokes equations in weighted spaces with singular forcing and applies the theory to derive error estimates for numerical approximations.

## Contribution

It introduces a weighted functional framework for the stationary Navier-Stokes equations with singular sources and demonstrates its use in error analysis.

## Key findings

- Existence of solutions in weighted spaces for 2D stationary Navier-Stokes
- Development of a priori error estimates for singular source approximations
- Application of Muckenhoupt weights in fluid dynamics analysis

## Abstract

In two dimensions, we show existence of solutions to the stationary Navier Stokes equations on weighted spaces $\mathbf{H}^1_0(\omega,\Omega) \times L^2(\omega,\Omega)$, where the weight belongs to the Muckenhoupt class $A_2$. We show how this theory can be applied to obtain a priori error estimates for approximations of the solution to the Navier Stokes problem with singular sources.