Global well-posedness for the Benjamin equation in low regularity

Details Global well-posedness for the Benjamin equation in low regularity Global well-posedness for the Benjamin equation in low regularity

2009-10-23

arxiv.org/abs/0910.4533v1

Mathematics

Analysis of PDEs

29 pages

Scientific paper

In this paper we consider the initial value problem of the Benjamin equation $$ \partial_{t}u+\nu \H(\partial^2_xu) +\mu\partial_{x}^{3}u+\partial_xu^2=0, $$ where $u:\R\times [0,T]\mapsto \R$, and the constants $\nu,\mu\in \R,\mu\neq0$. We use the I-method to show that it is globally well-posed in Sobolev spaces $H^s(\R)$ for $s>-3/4$. Moreover, we use some argument to obtain a good estimative for the lifetime of the local solution, and employ some multiplier decomposition argument to construct the almost conserved quantities.

Affiliated with

Also associated with

No associations

Rating

Global well-posedness for the Benjamin equation in low regularity 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 Global well-posedness for the Benjamin equation in low regularity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global well-posedness for the Benjamin equation in low regularity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-423821