Global Smoothing for the Periodic KdV Evolution
By Burak Erdogan, Nikolaos Tzirakis. 2011
92 citations recorded by the source corpus.
The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for H-s initial data, s > -1/2, and for any s(1) = 0. Our result and a theorem of Oskolkov for the Airy evolution imply that if one starts with continuous and bounded variation initial data, then the solution of KdV (given by the L-2 theory of Bourgain) is a continuous function of space and time. In addition, we demonstrate smoothing for the defocusing modified KdV equation on the torus for s > 1/2.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b6bbb1ca52e6d473729a1102202e0778f1613dbf
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In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Smoothing and global attractors for the Zakharov system on the torus (2012, methodology): “Here the method is applied to a dispersive system of equations where the resonances are harder to control and the coupling nonlinear terms introduce additional difficulties in estimating the first order corrections.”
- Regularity properties of the cubic nonlinear Schr\"odinger equation on the half line (2015, unknown): “, [10], [14], [21], [16], [13], [22].”