What are some real-world examples of compressible fluid mechanics in action?

[dcs23]

Hi Guys,

I know that the compressible Euler Equations are:

$$\partial_t (\rho \mathbf u) + (\mathbf u \cdot \nabla)(\rho \mathbf u) + \nabla p = 0$$

$$\partial_t \rho + \nabla \cdot (\rho \mathbf u) = 0$$

Subject to suitable initial conditions and solving for $$\mathbf u, \; \rho$$ unknown.

Does anybody have an example of a pair of functions which satisfies these relations in a non-1D case?

 

[dcs23]

Non trivial solutions would also be nice