Geodesic
A note on local smoothing effects for the unitary group associated with the KdV equation
Electronic journal of differential equations, Tome 2008 (2008)
In this note we show interesting local smoothing effects for the unitary group associated to Korteweg-de Vries type equation. Our main tools are the Hardy-Littlewood-Sobolev and Hausdorff-Young inequalities. Using our local smoothing effect and a dual version, we estimate the growth of the norm of solutions of the complex modified KdV equation.
Classification : 35A07, 35Q53
Keywords: modified KdV equation, KdV equation, local smoothing effect 
@article{EJDE_2008__2008__a77,
     author = {Carvajal,  Xavier},
     title = {A note on local smoothing effects for the unitary group associated with the {KdV} equation},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1173.35652},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a77/}
}
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Carvajal,  Xavier. A note on local smoothing effects for the unitary group associated with the KdV equation. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a77/