Well-posedness and parabolic smoothing effect for higher order Schrödinger type equations with constant coefficients

Abstract

We consider the Cauchy problem of a class of higher order Schrödinger type equations with constant coefficients. By employing the energy inequality, we show the $L^2$ 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.

19 pages, some notation changed, to appear in Osaka J. Math