Channel-localized Strichartz estimates of radial wave equations

Abstract: In this work we give a few new Strichartz estimates of radial solutions to the wave equation. These Strichartz estimates still use $L^p L<sup>q$ type norms in each channel-like region ${(x,t): |t|+2^k &lt; |x| &lt; |t|+2<sup>{k+1}}$, with weaker restrictions on $p, q$ than the classic ones, but combine these localized norms together in the way of an $l<sup>2$ space. We also give an application of these Strichartz estimates on the well-posedness theory of non-linear wave equations.