Exterior scattering of non-radial solutions to energy subcritical wave equations (2009.13991v1)

Abstract: We consider the defocusing, energy subcritical wave equation $\partial_t^2 u - \Delta u = -|u|^{p-1} u$ in dimension $d \in {3,4,5}$ and prove the exterior scattering of solutions if $3\leq d \leq 5$ and $1+6/d<p\<1+4/(d-2)$. More precisely, given any solution with a finite energy, there exists a solution $u_L$ to the homogeneous linear wave equation, so that the following limit holds \[ \lim_{t\rightarrow +\infty} \int_{|x|>t+R} |\nabla_{x,t} u(x,t)- \nabla_{x,t} u_L(x,t)|^2 dx = 0 ] for any fixed real number $R$. This generalize the previously known exterior scattering result in the radial case.