A SYMPLECTIC NON-SQUEEZING THEOREM FOR BBM EQUATION

Abstract

We study the initial value problem for the BBM equation:We prove that the BBM equation is globaly well-posed on H s (T) for s ≥ 0 and a symplectic non-squeezing theorem on H 1/2 (T).That is to say the flow-map u 0 → u(t) that associates to initial data u 0 ∈ H 1/2 (T) the solution u cannot send a ball into a symplectic cylinder of smaller width.Contents 1. Introduction 289 2. Symplectic capacities in Hilbert spaces and non-squeezing theorem 290 3. Application to the BBM equation 298