Remarks on the weak formulation of the Navier-Stokes equations on the 2D hyperbolic space

The Leray-Hopf solutions to the Navier-Stokes equation are known to be unique on ${\mathbb{R}}^2$. In our previous work we showed the breakdown of uniqueness in a hyperbolic setting. In this article, we show how to formulate the problem in order so the uniqueness can be restored.