Generation of vorticity near the boundary in planar Navier-Stokes flows
This is an interesting paper, concerned with rigorously constructing two- dimensional solutions to the Navier-Stokes equations with vorticity production on the boundary: it is closely connected to the fundamental work of \textit{A. J. Chorin} on the vortex method [J. Fluid Mech. 57, 785- 796 (1973)]. The writers determine rigorous estimates of the rate of production of vorticity due to the boundary for the case of a half plane, and provide a mathematical justification of the fact that the boundary behaves as a singular source of vorticity. The procedure is to approximate the Navier-Stokes equations by a convergent sequence of linear problems. In each linear problem the correct boundary conditions are satisfied by a vortex sheet on the boundary. The key to the paper is that the sequence of vortex sheets converges to a limit which describes the rate of vorticity production near the boundary. The convergence proof gives rise to explicit estimates of this vorticity production.
Navier-Stokes equations with vorticity production on the boundary
scientific article; zbMATH DE number 3949983