A symplectic non-squeezing theorem for BBM equation

Details A symplectic non-squeezing theorem for BBM equation A symplectic non-squeezing theorem for BBM equation

2010-07-08

arxiv.org/abs/1007.1359v2

Mathematics

Analysis of PDEs

Scientific paper

We study the initial value problem for the BBM equation: $$\left\{\begin{array}{l} u_t+u_x+uu_x-u_{txx}=0 \qquad x\in \T, t \in \R u(0,x)=u_0(x) \end{array} \right. .$$ We prove that the BBM equation is globaly well-posed on $H^s(\T)$ for $s\geq0$ and a symplectic non-squeezing theorem on $H^{1/2}(\T)$. That is to say the flow-map $u_0 \mapsto u(t)$ that associates to initial data $u_0 \in H^{1/2}(\T)$ the solution $u$ cannot send a ball into a symplectic cylinder of smaller width.

Affiliated with

Also associated with

No associations

Rating

A symplectic non-squeezing theorem for BBM equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A symplectic non-squeezing theorem for BBM equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A symplectic non-squeezing theorem for BBM equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-102920