In this paper, 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.
The first author was supported by RIKEN Junior Research Associate Program and JSPS KAKENHI Grant Number JP20J12750. The second author was supported by JSPS KAKENHI Grant Number 17K05316.
"Well-posedness and parabolic smoothing effect for higher order Schrödinger type equations with constant coefficients." Osaka J. Math. 59 (2) 465 - 480, April 2022.