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Open Access Research

The local well-posedness for nonlinear fourth-order Schrödinger equation with mass-critical nonlinearity and derivative

Cuihua Guo1*, Shulin Sun2 and Hongping Ren3

Author Affiliations

1 School of Mathematical Science, Shanxi University, Taiyuan, Shanxi, 030006, China

2 School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi, 041004, China

3 School of Applied Science, Taiyuan University of Science and Technology, Taiyuan, 030024, China

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Boundary Value Problems 2014, 2014:90  doi:10.1186/1687-2770-2014-90

Published: 6 May 2014

Abstract

We study the Cauchy problem of the nonlinear fourth-order Schrödinger equation with mass-critical nonlinearity and derivative: <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/90/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/90/mathml/M1">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/90/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/90/mathml/M2">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/90/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/90/mathml/M3">View MathML</a>, where a, b, and c are real numbers. We obtain the local well-posedness for the Cauchy problem with low regularity initial value data by the Fourier restriction norm method.

Keywords:
nonlinear fourth-order Schrödinger equation with derivative; Fourier restriction norm method; Cauchy problem