Existence of solutions of the \(g\)-Navier-Stokes equations (Q1880538)

The \textit{g}-Navier-Stokes equations in spatial dimension 2 are the following equations \[ \frac{\partial u}{\partial t}-\nu\Delta u+(u\cdot\nabla)u+\nabla p=f, \] with the continuity equation \[ \frac{1}{g}\nabla\cdot(gu)=0. \] Here, it is shown the existence and uniqueness of solutions of \textit{g}-Navier-Stokes equations on \(\mathbb R^{n}\) for \(n=2,3.\)