Shock wave

Summary

In the theory of conservation laws, a shock wave is a jump discontinuity of a weak solution that moves along a curve in spacetime. Its speed is fixed by the Rankine–Hugoniot conditions, and an entropy condition decides which jumps are physically admissible. Shocks form in finite time from smooth data in nonlinear equations such as Burgers' equation, so they are unavoidable in the theory. They model the sudden jumps of pressure and density in gas dynamics, such as the shock in front of a supersonic aircraft. See the definition.