Famous PDEs, the Navier-Stokes' equations
Another example is the set of
Navier-Stokes equations for incompressible, viscous flow
$$
\begin{equation*}
\frac{\partial \mathbf{u}}{\partial t} +\mathbf{u}\nabla\mathbf{u}-\Delta \mathbf{u}= -Dp; \hspace{1cm} \mathrm{div} \mathbf{u} = 0.
\end{equation*}
$$