# Non-uniqueness of weak solutions to 2D hypoviscous Navier-Stokes equations

## TL;DR

This paper demonstrates that in two dimensions, weak solutions to hypoviscous Navier-Stokes equations are not unique, using an adapted convex integration method.

## Contribution

It introduces a convex integration approach to show non-uniqueness of weak solutions for 2D hypoviscous Navier-Stokes equations.

## Key findings

- Weak solutions are non-unique in 2D hypoviscous Navier-Stokes.
- Convex integration can be adapted to 2D to prove non-uniqueness.

## Abstract

Through an adaption of the convex integration scheme in the two dimensional case, the non-uniqueness of $C^0_t L^2_x$ weak solutions is presented for the two-dimensional hypoviscous incompressible Navier-Stokes equations.