Minimal mass blow-up solutions for nonlinear Schrödinger equations with a potential

Naoki Matsui

Type: Article

Publication Date: 2023-06-01

Citations: 0

DOI: https://doi.org/10.2748/tmj.20211216

Abstract

We consider a mass critical nonlinear Schrödinger equation with a real-valued potential. In this work, we construct a minimal mass solution that blows up at finite time, under weaker assumptions on spatial dimensions and potentials than Banica, Carles, and Duyckaerts (2011). Moreover, we show that the blow-up solution converges to a blow-up profile. Furthermore, we improve some parts of the arguments in Raphaël and Szeftel (2011) and Le Coz, Martel, and Raphaël (2016).

Locations

Tohoku Mathematical Journal - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (11)

Action	Title	Year	Authors
+	Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power	1993	Franck Merle
+	Lyapunov stability of ground states of nonlinear dispersive evolution equations	1986	Michael I. Weinstein
+	Uniqueness of positive solutions of Δu−u+up=0 in Rn	1989	Man Kam Kwong
+ PDF Chat	Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS	2010	Pierre Raphaël Jérémie Szeftel
+	Nonlinear Schr�dinger equations and sharp interpolation estimates	1983	Michael I. Weinstein
+	Nonlinear scalar field equations, I existence of a ground state	1983	Henri Berestycki P. L. Lions
+	On universality of blow-up profile for L 2 critical nonlinear Schr�dinger equation	2004	Frank Merle Pierre Raphaël
+ PDF Chat	The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation	2005	Frank Merle Pierre Raphaël
+ PDF Chat	Minimal mass blow up solutions for a double power nonlinear Schrödinger equation	2016	Stefan Le Coz Yvan Martel Pierre Raphaël
+	On a sharp lower bound on the blow-up rate for the 𝐿² critical nonlinear Schrödinger equation	2005	Frank Merle Pierre Raphaël