Weighted Strichartz estimates with angular regularity and their applications

By Daoyuan Fang, Chengbo Wang. 2008

93 citations recorded by the source corpus.

Abstract 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 ≤ n ≤ 4, and a result of global well-posedness with small data for some nonlinear Schrödinger equation with L 2-subcritical nonlinearity.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/71e4cb33e4369baddaf5678390923bef1432ea04

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Concerning the wave equation on asymptotically Euclidean manifolds (2008, background): “Recently, Bony and Häfner [3] obtained a weaker version of KSS estimate in the current setting and proved the long time existence for quadratic semilinear wave equations with small data.”
On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles (2008, background): “A key step in the proof of Theorem 1.4 will be to establish the following result that is implicit in [4].”
Strichartz Estimates in Spherical Coordinates (2012, unknown): “3) was shown for ω(ρ) = ρ, 1 q < (n − 1)((1) 2 − 1 p ), q ≥ 2 and α ≥ 1 q by utilizing Rodnianski’s argument of [30] and weighted Strichartz estimates (see [11, 14, 7]).”
On the Cauchy Problem of Fractional Schrödinger Equation with Hartree Type Nonlinearity (2012, background): “6) we refer to [2] and also to [11, 7] for earlier and more general versions, respectively.”