Geodesic
Ill-posedness for periodic nonlinear dispersive equations
Electronic Journal of Differential Equations, Tome 2010 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 76B25, 35Q51, 35Q53
Keywords: ill-posedness, mkdv equation, defocusing mkdv equation, BO equation, higher order evolutions equations 
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     author = {Pava, Jaime Angulo and Hakkaev, Sevdzhan},
     title = {Ill-posedness for periodic nonlinear dispersive equations},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2010},
     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a264/}
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Pava, Jaime Angulo; Hakkaev, Sevdzhan. Ill-posedness for periodic nonlinear dispersive equations. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a264/