Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation

Abstract

The endpoint Strichartz estimates for the Schrödinger equation are known to be false in two dimensions. However, if one averages the solution in $L^2$ in the angular variable, we show that the homogeneous endpoint and the retarded half-endpoint estimates hold, but the full retarded endpoint fails. In particular, the original versions of these estimates hold for radial data.

8 pages, minor typos corrected

Cited by in corpus (15)

• Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schroedinger maps on R^2
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• The cubic Dirac equation: Small initial data in $H^1({\mathbb{R}}^3)$
• Some Remarks on Strichartz Estimates for Homogeneous Wave Equation
• Strichartz Estimates in Spherical Coordinates
• Sharp Strichartz estimates on non-trapping asymptotically conic manifolds
• Generic and non-generic behavior of solutions to the defocusing energy critical wave equation with potential in the radial case
• Remarks on endpoint Strichartz estimates for Schrödinger equations with the critical inverse-square potential
• Inhomogeneous Strichartz estimates with spherical symmetry and applications to the Dirac-Klein-Gordon system in two space dimensions
• Decay Estimates and Strichartz Estimates of Fourth-order Schrödinger Operator
• Asymptotic stability of harmonic maps under the Schrödinger flow
• Strichartz estimates for the kinetic transport equation
• Spherical Averaged Endpoint Strichartz Estimates for The Two-dimensional Schrodinger Equations with Inverse Square Potential
• Singular integrals with angular integrability
• Well-posedness for the Cauchy problem of spatially weighted dissipative equation