Weighted Strichartz Estimates with Angular Regularity and their Applications

In this paper, we establish an optimal dual version of trace estimate involving angular regularity. Based on this estimate, we get the generalized Morawetz estimates and weighted Strichartz estimates for the solutions to a large class of evolution equations, including the wave and Schrödinger equation. As applications, we prove the Strauss' conjecture with a kind of mild rough data for $2\le n\le 4$, and a result of global well-posedness with small data for some nonlinear Schrödinger equation with $L^2$-subcritical nonlinearity.

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