Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations

Details Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations

2008-02-07

arxiv.org/abs/0802.1039v1

Mathematics

Analysis of PDEs

Scientific paper

We study the Cauchy problem for the dissipative Benjamin-Ono equations $u_t+\H u_{xx}+|D|^\alpha u+uu_x=0$ with $0\leq\alpha\leq 2$. When $0\leq\alpha< 1$, we show the ill-posedness in $H^s(\R)$, $s\in\R$, in the sense that the flow map $u_0\mapsto u$ (if it exists) fails to be $\C^2$ at the origin. For $1<\alpha\leq 2$, we prove the global well-posedness in $H^s(\R)$, $s>-\alpha/4$. It turns out that this index is optimal.

Affiliated with

Also associated with

No associations

Rating

Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations 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 Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-365387