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Famous PDEs, Euler's equations

Similarly, famous systems of non-linear partial differential equations are for example Euler's equations for incompressible, inviscid flow \begin{equation*} \frac{\partial \mathbf{u}}{\partial t} +\mathbf{u}\nabla\mathbf{u}= -Dp; \hspace{1cm} \mathrm{div} \mathbf{u} = 0, \end{equation*} with p being the pressure and \begin{equation*} \nabla = \frac{\partial}{\partial x}e_x+\frac{\partial}{\partial y}e_y, \end{equation*} in the two dimensions. The unit vectors are e_x and e_y .