On the inhomogeneous biharmonic nonlinear Schrodinger equation: Local, global and stability results

Author(s)

Guzman, Carlos M. ^[1] ; Pastor, Ademir ^[2]

Affiliation

^[1] Fluminense Fed Univ, Dept Math, Niteroi, RJ - Brazil

^[2] Univ Estadual Campinas, IMECC, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 56, DEC 2020.
• Web of Science Citations: 0

Abstract

We consider the inhomogeneous biharmonic nonlinear Schrodinger equation (IBNLS) iu(t) +Delta(2)u +lambda vertical bar x vertical bar(-b)vertical bar u vertical bar(alpha) u = 0, where lambda = +/- 1 and alpha, b > 0. We show local and global well-posedness in H-s(R-N) in the H-s-subcritical case, with s = 0, 2. Moreover, we prove a stability result in H-2(R-N), in the mass-supercritical and energy-subcritical case. The fundamental tools to prove these results are the standard Strichartz estimates related to the linear problem. (C) 2020 Elsevier Ltd. All rights reserved. (AU)

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