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An approximation method for the cauchy problem to the three‐dimensional equation of vorticity transport
Author(s) -
Hebeker F.K.,
Martensen E.
Publication year - 1983
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670050128
Subject(s) - vorticity , mathematics , constructive , cauchy problem , mathematical analysis , initial value problem , sequence (biology) , vorticity equation , vortex , physics , process (computing) , genetics , biology , computer science , thermodynamics , operating system
The vorticity problem (V 0 ) 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 (V ϵ ), ϵ > 0, possessing a unique classical solution globally in time. For (V ϵ ) a constructive approximation method is introduced. This procedure yields a sequence (ω n ϵ ) of approximate vorticity fields, converging to the global solution of (V ϵ ) and to the local solution of (V 0 ).