On persistence of spatial analyticity for the dispersion-generalized periodic KdV equation. (December 2017) - Himonas, A. Alexandrou; Kalisch, Henrik; Selberg, Sigmund
Abstract: Persistence of spatial analyticity is studied for periodic solutions of the dispersion-generalized KdV equation u t − | D x | α u x + u u x = 0 for α ≥ 2 . For a class of analytic initial data with a uniform radius of analyticity σ 0 > 0, we obtain an asymptotic lower bound σ ( t ) ≥ c t − p on the uniform radius of analyticity σ ( t ) at time t, as t → ∞, where p = max ( 1, 4 / α ) . The proof relies on bilinear estimates in Bourgain spaces and an approximate conservation law.