Electro-magneto-static study of the nonlinear Schrödinger equation coupled with Bopp-Podolsky electrodynamics in the Proca setting

Emmanuel Hebey

doi:10.3934/dcds.2019291

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2019, Volume 39, Issue 11: 6683-6712. Doi: 10.3934/dcds.2019291

This issue Previous Article Global large smooth solutions for 3-D Hall-magnetohydrodynamics Next Article Global well-posedness to the cauchy problem of two-dimensional density-dependent boussinesq equations with large initial data and vacuum

Electro-magneto-static study of the nonlinear Schrödinger equation coupled with Bopp-Podolsky electrodynamics in the Proca setting

Emmanuel Hebey

Emmanuel Hebey, Université de Cergy-Pontoise, Département de Mathématiques, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France

Received: February 28, 2019

Revised: May 31, 2019

Published: August 2019

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We investigate the system consisting of the the nonlinear Schrödinger equation coupled with Bopp-Podolsky electrodynamics in the Proca setting in the context of closed $ 3 $-dimensional manifolds. We prove existence of solutions up to the gauge, and compactness of the system both in the subcritical and in the critical case.

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Mathematics Subject Classification: 35G50, 58J99.

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