Electron. J. Diff. Equ., Vol. 2011 (2011), No. 168, pp. 1-11.

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

Shigeo Tarama

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.

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Shigeo Tarama
Lab. of Applied Mathematics, Faculty of Engineering
Osaka City University, Osaka 558-8585, Japan
email: starama@mech.eng.osaka-cu.ac.jp

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