A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results

Details A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results

2011-08-18

arxiv.org/abs/1108.3714v1

Mathematics

Analysis of PDEs

Scientific paper

We consider the generalized two-dimensional Zakharov-Kuznetsov equation $u_t+\partial_x \Delta u+\partial_x(u^{k+1})=0$, where $k\geq3$ is an integer number. For $k\geq8$ we prove local well-posedness in the $L^2$-based Sobolev spaces $H^s(\mathbb{R}^2)$, where $s$ is greater than the critical scaling index $s_k=1-2/k$. For $k\geq 3$ we also establish a sharp criteria to obtain global $H^1(\R^2)$ solutions. A nonlinear scattering result in $H^1(\R^2)$ is also established assuming the initial data is small and belongs to a suitable Lebesgue space.

Affiliated with

Also associated with

No associations

Rating

A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results 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 note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-181219