COUNTEREXAMPLES TO STRICHARTZ ESTIMATES FOR THE MAGNETIC SCHRÖDINGER EQUATION

DOI10.1142/S0219199711004245zbMath1227.35102arXiv0904.1129OpenAlexW2114146096WikidataQ124880184 ScholiaQ124880184MaRDI QIDQ3002638

Andoni García, Luca Fanelli

Publication date: 23 May 2011

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.1129

zbMATH Keywords

magnetic potentialdispersive equationsCoulomb decay behaviorpurely magnetic Schrödinger operator

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) A priori estimates in context of PDEs (35B45) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (13)

Dispersive estimates for 2D-wave equations with critical potentials ⋮ Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials ⋮ Time decay of scaling critical electromagnetic Schrödinger flows ⋮ The forward problem for the electromagnetic Helmholtz equation with critical singularities ⋮ Semilinear Schrödinger equations with a critical scale of the singular electromagnetic field ⋮ On the lack of dispersion for a class of magnetic Dirac flows ⋮ Energy scattering theory for electromagnetic NLS in dimension two ⋮ Energy concentration and explicit Sommerfeld radiation condition for the electromagnetic Helmholtz equation ⋮ Dispersive estimates for the Dirac equation in an Aharonov-Bohm field ⋮ Hankel transforms and weak dispersion ⋮ Decay and Strichartz estimates in critical electromagnetic fields ⋮ Unique continuation for the magnetic Schrödinger operator with singular potentials ⋮ Time decay of scaling invariant electromagnetic Schrödinger equations on the plane

Cites Work

• Magnetic virial identities, weak dispersion and Strichartz inequalities
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Generalized Strichartz inequalities for the wave equation
• Spectral analysis of Schrödinger operators with magnetic fields
• Strichartz and Smoothing Estimates for Dispersive Equations with Magnetic Potentials
• Endpoint Strichartz estimates

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