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Vortex reconnection in the three dimensional Navier-Stokes equations. (English) Zbl 1381.35117

Summary: We prove that the vortex structures of solutions to the 3D Navier-Stokes equations can change their topology without any loss of regularity. More precisely, we construct smooth high-frequency solutions to the Navier-Stokes equations where vortex lines and vortex tubes of arbitrarily complicated topologies are created and destroyed in arbitrarily small times. This instance of vortex reconnection is structurally stable and in perfect agreement with the existing computer simulations and experiments. We also provide a (non-structurally stable) scenario where the destruction of vortex structures is instantaneous.

MSC:

35Q30 Navier-Stokes equations
35Q31 Euler equations
76D05 Navier-Stokes equations for incompressible viscous fluids
76D17 Viscous vortex flows
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