Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 168, pp. 1-11.

Title: L2-well-posed Cauchy problem for fourth-order dispersive
       equations on the line

Author: Shigeo Tarama (Osaka City Univ., Osaka, Japan)

Abstract: 
 Mizuhara [2] obtained conditions for the Cauchy
 problem of a fourth-order dispersive operator to be well
 posed in the $L^2$ sense. Two of those conditions
 were shown to be necessary under additional assumptions.
 In this article, we prove the necessity without the additional
 assumptions.

Submitted August 16, 2011. Published December 14, 2011.
Math Subject Classifications: 37L50, 16D10.
Key Words: Dispersive operators; Cauchy problem; well posed.