# Navier-Stokes equations #fluid-mechanics #turbulence The incompressible Navier-Stokes equations read: $\frac{\partial u_i}{\partial t} + u_j\frac{\partial u_i}{\partial x_j} = -\frac{1}{\rho}\frac{\partial p}{\partial x_i} + \nu\frac{\partial^2 u_i}{\partial x_j\partial x_j}$ ^ec02dc