On a dynamical system related to fluid mechanics
The authors discuss a dynamical system strictly related to fluid mechanics and defined by the equation of motion of \(N\) point vortices. The time evolution of the system has been studied on a qualitative level and properties of collapse and chaoticity are discovered. The authors also investigate the connection of this dynamical system with a system of \(N\) concentrated smoke rings in an incompressible inviscid fluid, with an axial symmetry without swirl. The convergence of the velocity to the vector field of the system is analyzed and it is proved rigorously at time zero and for any \(N\). The same result is extended to any time in the case of smoke ring.
scientific article; zbMATH DE number 1406554