Dynamics of Partial Differential Equations

Volume 7 (2010)

Number 2

Limiting profile of the blow-up solutions for the fourth-order nonlinear Schrödinger equation

Pages: 187 – 205

DOI: http://dx.doi.org/10.4310/DPDE.2010.v7.n2.a4

Authors

Han Yang (College of Mathematics, Southwest Jiaotong University, Chengdu, China)

Jian Zhang (Visual Computing and Vitual Reality Key Laboratory, Sichuan Normal University, Chengdu, China)

Shihui Zhu (Visual Computing and Vitual Reality Key Laboratory, Sichuan Normal University, Chengdu, China)

Abstract

This paper is concerned with the blow-up solutions of the focusing fourth-order mass-critical nonlinear Schrödinger equation. Establishing the profile decomposition of the bounded sequences in H², we obtain the variational characteristics of the corresponding ground state and a compactness lemma. Moreover, we obtain the L²-concentration of the blow-up solutions and the limiting profile of the minimal mass blow-up solutions in the general case.

Keywords

nonlinear Schrödinger equation, Blow-up solution, Profile decomposition, Limiting profile

2010 Mathematics Subject Classification

35B44, 35Q55

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