Global Smoothing for the Periodic KdV Evolution
Global Smoothing for the Periodic KdV Evolution
The Korteweg–de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for Hs initial data, , and for any , the difference of the nonlinear and linear evolutions is in Hs1 for all times, with at most polynomially growing Hs1 norm. The result also extends to …