Interaction of point sources and vortices for incompressible planar fluids

Details Interaction of point sources and vortices for incompressible planar fluids Interaction of point sources and vortices for incompressible planar fluids

2008-12-19

arxiv.org/abs/0812.3894v2

Qualitative Theory of Dynamical Systems, Vol.8, No.2, pp. 371-379, 2010

Physics

Mathematical Physics

9 pages

Scientific paper

10.1007/s12346-010-0015-8

We consider a new system of differential equations which is at the same time gradient and locally Hamiltonian. It is obtained by just replacing a factor in the equations of interaction for N point vortices, and it is interpreted as an interaction of N point sources. Because of the local Hamiltonian structure and the symmetries it obeys, it does possess some of the first integrals that appear in the N vortex problem. We will show that binary collisions are easily blown up in this case since the equations of motion are of first order. This method may be easily generalized to the blow up of higher order collisions. We then generalize the model further to interactions of sources and vortices.

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