WELL-POSEDNESS AND PARABOLIC SMOOTHING EFFECT FOR HIGHER ORDER SCHRO¨ DINGER TYPE EQUATIONS WITH CONSTANT COEFFICIENTS

In this paper, we consider the Cauchy problem of a class of higher order Schr¨odinger type equations with constant coefficients. By employing the energy inequality, we show the L2 well-posedness, the parabolic smoothing and a breakdown of the persistence of regularity. We classify this class of equations into three types on the basis of their smoothing property