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We study the Cauchy problem of the nonlinear fourth-order Schrödinger equation with mass-critical nonlinearity and derivative: iut+auxxxx+bu2u¯xx+c|u|8u=0, x∈R, t∈R, 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.

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