A quaternionic treatment of Navier-Stokes equations. (English) Zbl 0751.76022

Gürlebeck, Klaus; Sprößig, Wolfgang

Geometry and physics, Proc. 9th Winter Sch., Srní/Czech. 1989, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 22, 77-95 (1990).

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[For the entire collection see Zbl 0699.00032.]
Authors attempt to solve the steady state Navier-Stokes (N-S) equations by using a quaternionic approach. This method, first suggested by Oseen, involves replacing the unknown velocity field in the convective term operator, by a velocity vector which solves the Stokes problem.
The paper is very theoretical and is presented in the form of a sequence of theorems and subsequent proofs. The main contribution is in the treatment of theoretical applied mathematics/fluid dynamics problems, with an attempt to introduce numerical solutions of the boundary value problem of the N-S equations.

Reviewer: S.Carmi (Philadelphia)

MSC:

76D05	Navier-Stokes equations for incompressible viscous fluids
76D07	Stokes and related (Oseen, etc.) flows
35Q30	Navier-Stokes equations
15B33	Matrices over special rings (quaternions, finite fields, etc.)

Keywords:

Stokes problem; numerical solutions

Citations:

Zbl 0699.00032