Some remarks on the inhomogeneous biharmonic NLS equation. (October 2022)

• Record Type: Journal Article
• Authors: Guzmán, Carlos M.; Pastor, Ademir
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: Inhomogeneous biharmonic nonlinear Schrödinger equation -- Global well-posedness -- Critical nonlinearity -- Stability theory; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103643
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider the inhomogeneous biharmonic nonlinear Schrödinger equation i u t + Δ 2 u + λ | x | − b | u | α u = 0, where λ = ± 1 and α, b > 0 . In the subctritical case, we improve the global well-posedness result obtained in Guzmán and Pastor (2020) for dimensions N = 5, 6, 7 in the Sobolev space H 2 ( R N ) . The fundamental tools to establish our results are the standard Strichartz estimates related to the linear problem and the Hardy-Littlewood inequality. Results concerning the energy-critical case, that is, α = 8 − 2 b N − 4 are also reported. More precisely, we show well-posedness and a stability result with initial data in the critical space H ̇ 2 .