Weighted Strichartz Estimates with Angular Regularity and their Applications

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

Final version (corrected some typos). To appear in Forum Mathematicum

References in corpus (6)

• Ill-posedness for nonlinear Schrodinger and wave equations
• Some Remarks on Strichartz Estimates for Homogeneous Wave Equation
• Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case
• Local Existence for Nonlinear Wave Equation with Radial Data in 2+1 Dimensions
• Nonlinear Schroedinger equations with radially symmetric data of critical regularity
• On Abstract Strichartz Estimates and the Strauss Conjecture for Nontrapping Obstacles

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