# Damped DNLW

The damped DNLW

${\displaystyle \Box u=u^{2}u_{t}}$

in three dimensions is known to be locally well-posed in any sub-critical regularity ${\displaystyle s>1}$, and has scattering in ${\displaystyle H^{3}}$ Smh-p. It would be interesting to see whether one has local well-posedness in the critical energy regularity ${\displaystyle H^{1}}$. It is an example of a linear-derivative nonlinear wave equation.