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 $L^p{L}^q$ type norms in each channel-like region $\{(x,t):|t|+2^k<|x|<|t|+2^{k+1}\}$, with weaker restrictions on $p,q$ than the classic ones, but combine these localized norms together in the way of an $l^2$ space. We also give an application of these Strichartz estimates on the well-posedness theory of non-linear wave equations.

17 pages, 1 figure