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

Hebeker F.K. | Zendy; Martensen E. | Zendy

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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 ).

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