On the lack of dispersion for a class of magnetic Dirac flows

2011/07/05 by Naiara Arrizabalaga, Arrizabalaga, Naiara, Luca Fanelli +3
Mathematics · #35L05 #35Q40 #58J50 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1107.0843

openalex publication_date 2011/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that global Strichartz estimates for magnetic Dirac operators generally fails, if the potentials do not decay fast enough at infinity. In order to prove this, we construct some explicit examples of homogeneous magnetic potentials with less than Coulomb decay, i. e. with homogeneity-degree more than -1, such that the magnetic field points to a fixed direction, which does not depend on x∈ ℝ³.

Citations

• Space‐time estimates for null forms and the local existence theorem
• The quantum theory of the electron
• Strichartz estimates for the Wave and Schrodinger Equations with the Inverse-Square Potential

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