Well-posedness for the nonlinear fractional Schrodinger equation and inviscid limit behavior of solution for the fractional Ginzburg-Landau equation

The well-posedness for the Cauchy problem of the nonlinear fractional Schrodinger equation u(t) + i(-Delta)(alpha)u + i vertical bar u vertical bar(2)u = 0, (x, t) is an element of R-n x R, 1/2 < alpha < 1 is considered. The local well-posedness in subcritical space H-s with s > n/2 -alpha is obtained. Moreover, the inviscid limit behavior of solution for the fractional Ginzburg-Landau equation u(t) + (nu+i)(-Delta)(alpha)u + i vertical bar u vertical bar(2)u - 0 is also considered. It is shown that the solution of the fractional Ginzburg-Landau equation converges to the solution of nonlinear fractional Schrodinger equation in the natural space C([0, T]; H-s) with s > n/2 - alpha if nu tends to zero.