Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 119, pp. 1-19.

Title: Ill-posedness for periodic nonlinear dispersive equations

Authors: Jaime Angulo Pava (IME-USP, Sao Paulo, SP, Brazil)
         Sevdzhan Hakkaev (Shumen University, Bulgaria)

Abstract:
 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.