Blow-up solutions for a system of Schrödinger equations with general quadratic-type nonlinearities in dimensions five and six

2020/03/24 by Norman Noguera, Noguera, Norman, Ademir Pastor +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2003.11103

openalex publication_date 2020/03/24 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this work, we show the existence of ground state solutions for an l-component system of non-linear Schrödinger equations with quadratic-type growth interactions in the energy-critical case. They are obtained analyzing a critical Sobolev-type inequality and using the concentration-compactness method. As an application, we prove the existence of blow-up solutions of the system without the mass-resonance condition in dimension six (and five), when the initial data is radial.

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