# Navier-Stokes equation

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$\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}\right) = -\nabla p + \nabla \cdot\mathbb{T} + \mathbf{f},$
where $\mathbf{v}$ is the flow velocity, $\rho$ is the fluid density, p is the pressure, $\mathbb{T}$ is the stress tensor, and $\mathbf{f}$ represents body forces per unit volume acting on the fluid.