Generalized and weighted Strichartz estimates

Abstract

In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space ${\mathbb{R}}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of dispersive operators including the Schrödinger and wave equation. As a sample application of these new estimates, we are able to prove the Strauss conjecture with low regularity for dimension 2 and 3.

Final version, to appear in the Communications on Pure and Applied Analysis. 33 pages. 2 more references added

References in corpus (3)

• Some Remarks on Strichartz Estimates for Homogeneous Wave Equation
• Global existence for semilinear wave equations exterior to nontrapping obstacles
• Almost global existence for some semilinear wave equations with almost critical regularity

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