Jaime Angulo Pava, Sevdzhan Hakkaev
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.
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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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