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Famous PDEs, the Navier-Stokes' equations

Another example is the set of Navier-Stokes equations for incompressible, viscous flow \begin{equation*} \frac{\partial \mathbf{u}}{\partial t} +\mathbf{u}\nabla\mathbf{u}-\Delta \mathbf{u}= -Dp; \hspace{1cm} \mathrm{div} \mathbf{u} = 0. \end{equation*}