A symplectic non-squeezing theorem for BBM equation

作者：Roumegoux David^*

来源：Dynamics of Partial Differential Equations, 2010, 7(4): 289-305.

• BBM equation
• well-posedness
• symplectic non-squeezing theorem

We study the initial value problem for the BBM equation:
{u(t) + u(x) + uu(x) - u(txx) = 0 x is an element of T, t is an element of R
u(0, x) = u(0)(x)
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) (sic) u(t) that associates to initial data u(0) is an element of H(1/2)(T) the solution u cannot send a ball into a symplectic cylinder of smaller width.

• 出版日期2010-12