Long-time Strichartz estimates and applications

Abstract

In this section, we prove a long-time Strichartz inequality for solutions to (8.15) as described in Theorem 8.10. This will then be used to rule out rapid frequency cascade solutions, namely, solutions which also satisfy

$$ \int_0^{T_{\max } } {N\left( t \right)^{ - 1} \,dt\,<\;\infty }. $$