Well-posedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity
Well-posedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity
In the present paper, we consider the Cauchy problem of fourth order nonlinearSchrödinger type equations with derivative nonlinearity.In one dimensional case, the small data global well-posedness and scattering for the fourth order nonlinear Schrödinger equation with the nonlinear term $\partial _x (\overline{u}^4)$ are shown in thescaling invariant space $\dot{H}^{-1/2}$.Furthermore, we …