Famous PDEs, Euler's equations
Similarly, famous systems of non-linear partial differential equations are for example Euler's equations for
incompressible, inviscid flow
∂u∂t+u∇u=−Dp;divu=0,
with
p being the pressure and
∇=∂∂xex+∂∂yey,
in the two dimensions. The unit vectors are
ex and
ey.