Blow-up for the 3D intercritical inhomogeneous NLS with inverse-square potential

2023/05/11 by Luccas Campos, Campos, Luccas, Mykael Cardoso +3
Mathematics · Physics and Astronomy · #35A01 #35B44 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.2305.06971

openalex publication_date 2023/05/11 · openalex created_date 2023/05/13 · openalex updated_date 2026/07/28

Abstract

In this paper we study the focusing inhomogeneous 3D nonlinear Schrödinger equation with inverse-square potential in the mass-supercritical and energy-subcritical regime. We first establish local well-posedness in H_a^s_c∩ H_a¹, with s_c=3/2-(2-b)/2σ. Next, we prove the blow-up of the scaling invariant Lebesgue norm for radial solutions and also, with an additional restriction, in the non-radial case.

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