Abstract
The Robin function has an important application in planar fluid dynamics. Consider an incompressible and non-viscous fluid. We will see that the interaction of point vortices with the walls of the container is governed by the Robin function, while the interaction of vortex pairs is governed by the Green’s function. As an application of the properties of the Robin function derived in the previous chapters we prove long time existence of vortex pairs. This result is optimal, since three vortices can collide in finite time. We report from our work with B. Gustafsson [52].
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© 1999 Springer Basel AG
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Flucher, M. (1999). Vortex Motion in Two Dimensional Hydrodynamics. In: Variational Problems with Concentration. Progress in Nonlinear Differential Equations and Their Applications, vol 36. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8687-1_15
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DOI: https://doi.org/10.1007/978-3-0348-8687-1_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9729-7
Online ISBN: 978-3-0348-8687-1
eBook Packages: Springer Book Archive