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Consider the Navier-Stokes equations $$\frac{\partial \bf{u}}{\partial t}+\bf{u}\cdot\nabla \bf{u}=-\nabla p+\nu \nabla^2\bf{u}.$$ We can rewrite the inertial term as $$\bf{u}\cdot\nabla \bf{u}=\frac{1}{2}\bf{u}^2-\bf{u}\times\boldsymbol{\omega}.$$ Therefore, the Navier-Stokes equations can be rewritten as \frac{\partial \bf{u}}{\partial ...