Geodesic
Ill-posedness for periodic nonlinear dispersive equations
Electronic journal of differential equations, Tome 2010 (2010)
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 
@article{EJDE_2010__2010__a264,
     author = {Pava,  Jaime Angulo and Hakkaev,  Sevdzhan},
     title = {Ill-posedness for periodic nonlinear dispersive equations},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1402.35237},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a264/}
}
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AU  - Hakkaev,  Sevdzhan
TI  - Ill-posedness for periodic nonlinear dispersive equations
JO  - Electronic journal of differential equations
PY  - 2010
VL  - 2010
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%A Pava,  Jaime Angulo
%A Hakkaev,  Sevdzhan
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%J Electronic journal of differential equations
%D 2010
%V 2010
%U http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a264/
%G en
%F EJDE_2010__2010__a264
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/