Electron. J. Diff. Equ., Vol. 2010(2010), No. 119, pp. 1-19.

Ill-posedness for periodic nonlinear dispersive equations

Jaime Angulo Pava, Sevdzhan Hakkaev

In this article, we establish new results about the ill-posedness of the Cauchy problem for the modified Korteweg-de Vries and the defocusing modified Korteweg-de Vries equations, in the periodic case. The lack of local well-posedness is in the sense that the dependence of solutions upon initial data fails to be continuous. We also develop a method for obtaining ill-posedness results in the periodic and non-periodic cases for the equations in the hierarchies of these equations and also in the case of the Benjamin-Ono equation.

Submitted January 26, 2010. Published August 24, 2010.
Math Subject Classifications: 76B25, 35Q51, 35Q53.
Key Words: Ill-posedness, mKdV equation; defocusing mKdV equation; BO equation; higher order evolutions equations.

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Jaime Angulo Pava
Department of Mathematics, IME-USP
Rua do Matão 1010, Cidade Universitária
CEP 05508-090, São Paulo, SP, Brazil
email: angulo@ime.usp.br
Sevdzhan Hakkaev
Faculty of Mathematics and Informatics
Shumen University, 9712 Shumen, Bulgaria
email: shakkaev@fmi.shu-bg.net

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