On the regularization mechanism for the periodic Korteweg–de Vries equation
On the regularization mechanism for the periodic Korteweg–de Vries equation
Abstract In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg–de Vries (KdV) equation in the homogeneous Sobolev spaces Ḣ s for s ≥ 0. Specifically, we prove the global existence, uniqueness, and Lipschitz‐continuous dependence on the initial data of …