An approximation method for the cauchy problem to the three‐dimensional equation of vorticity transport

摘要

AbstractThe vorticity problem (V0) is shown to have (at least) locally in time a unique classical solution. For numerical purposes global solvability is desired. So by suitable operations we proceed to a family of modified vorticity problems (Vϵ), ϵ>0, possessing a unique classical solution globally in time.For (Vϵ) a constructive approximation method is introduced. This procedure yields a sequence (ω nϵ) of approximate vorticity fields, converging to the global solution of (Vϵ) and to the local solution