# Morawetz inequality

Morawetz inequalities are monotonicity formulae for nonlinear Schrodinger and wave equations, where the monotone quantity is usually generated by integrating the momentum density against a bounded vector field such as the outgoing spatial normal ${\displaystyle {\frac {x_{i}}{|x|}}}$. They are particularly useful for obtaining scattering results in Sobolev spaces such as the energy class.