Steady periodic gravity waves with surface tension

Details Steady periodic gravity waves with surface tension Steady periodic gravity waves with surface tension

2009-11-06

arxiv.org/abs/0911.1375v1

Mathematics

Analysis of PDEs

67 pages, 3 figures

Scientific paper

In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a gravitational force acting on the body of the fluid. We prove the existence of global continua of classical solutions that are periodic and traveling. This is accomplished by first constructing a 1-parameter family of laminar flow solutions, $\mathcal{T}$, then applying bifurcation theory methods to obtain local curves of small amplitude solutions branching from $\mathcal{T}$ at an eigenvalue of the linearized problem. Each solution curve is then continued globally by means of a degree theoretic theorem in the spirit of Rabinowitz. Finally, we complement the degree theoretic picture by proving an alternate global bifurcation theorem via the analytic continuation method of Dancer.

Affiliated with

Also associated with

No associations

Rating

Steady periodic gravity waves with surface tension 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 Steady periodic gravity waves with surface tension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Steady periodic gravity waves with surface tension will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-699374