Blow-up of non-radial solutions for the L2 critical inhomogeneous NLS equation. (4th August 2022)

• Record Type: Journal Article
• Authors: Cardoso, Mykael; Farah, Luiz Gustavo
• Is Part Of: Nonlinearity. Volume 35:Number 8(2022)
• Page Start: 4426
• Page End: 4436
• Publication Date: 2022-08-04
• Subjects: inhomogeneous NLS equation -- L2 critical -- blow-up -- non-radial solutions; 35Q55 -- 35B44; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac7b60
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider the L 2 critical inhomogeneous nonlinear Schrödinger equation in R N i ∂ t u + Δ u + | x | − b | u | 4 − 2 b N u = 0, where N ⩾ 1 and 0 < b < min{2, N }. We prove that if u 0 ∈ H 1 ( R N ) satisfies E [ u 0 ] < 0, then the corresponding solution blows-up in finite time. This is in sharp contrast to the classical L 2 critical nonlinear Schrödinger equation where this type of result is only known in the radial case for N ⩾ 2.