Hello,

The Navier-Stokes equations can be written on a riemannian manifold: $$\dot{u}+\nabla_u u+ \Delta u=(df)^* $$ $$d^* u=0$$ where $\nabla$ is the Levi-Civita connection, $u$ is a vector fields, $\Delta$ is the laplacian, $df$ is the differential of $f$, $(df)^* $ is the dual of $df$ by the metric, $d^*u$ is the divergence of $u$.

The problem is due to Antoine Balan.

Do you have references ?

Thanks in advance.