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