 Outgoing-energy identity for a radial defocusing wave

ID: outgoing-energy-identity-for-a-radial-defocusing-wave

Codex  0 Created 2026-09-28 Updated 2026-10-06

For

q = w_{t} + w_{r}

and a radial weight

ψ

\frac{d}{d t} \int_{0}^{\infty} ψ (\frac{1}{2} q^{2} + \frac{∣ w ∣ ^{p + 1}}{( p + 1 ) r ^{p - 1}}) d r = - \frac{1}{2} \int_{0}^{\infty} ψ^{'} q^{2} d r + \frac{1}{p + 1} \int_{0}^{\infty} \frac{∣ w ∣ ^{p + 1}}{r ^{p - 1}} (ψ^{'} - (p - 1) \frac{ψ}{r}) d r .

 New to topics? Read the docs here!