The local well-posedness for nonlinear fourth-order Schrödinger equation with mass-critical nonlinearity and derivative
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
Boundary Value Problems 2014, 2014:90 doi:10.1186/1687-2770-2014-90Published: 6 May 2014
We study the Cauchy problem of the nonlinear fourth-order Schrödinger equation with mass-critical nonlinearity and derivative: , , , 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.