Some remarks on the inhomogeneous biharmonic NLS equation

Author(s)

Guzman, Carlos M. ; Pastor, Ademir

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 67, p. 17-pg., 2022-10-01.

Abstract

We consider the inhomogeneous biharmonic nonlinear Schrodinger equation iu(t) + Delta(2)u + lambda vertical bar x vertical bar(-b)|u|(alpha)u = 0, where lambda = +/- 1 and alpha, b > 0. In the subctritical case, we improve the global wellposedness result obtained in Guzman 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, alpha = 8-2b/N-4 are also reported. More precisely, we show well-posedness and a stability result with initial data in the critical space H-2. (C) 2022 Published by Elsevier Ltd. (AU)

• FAPESP's process: 19/02512-5 - Systems and partial differential equations
• Grantee: Marcelo da Silva Montenegro
• Support Opportunities: Research Projects - Thematic Grants