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Uncoupled solution of the three-dimensional vorticity-velocity equations. (English) Zbl 0912.35124
The three-dimensional incompressible Navier-Stokes equations in the vorticity-velocity representation are studied.
Using some uncoupling techniques the existence of a unique solution is shown. The analysis is performed for the case of the underlying Stokes system, without loss of generality. The underlying technique relies upon the splitting of the vorticity \(\omega\) into a sum of the form \(\omega= \omega_0+\omega_J\), where \(\omega_0\) fulfills homogeneous Dirichlet boundary conditions for its tangential components and \(\omega_J\) is harmonic. Only a scalar boundary value problem needs to be solved to determine a harmonic component of the vorticity \(\omega_J\) for uncoupled formulations.

35Q30 Navier-Stokes equations
76D07 Stokes and related (Oseen, etc.) flows
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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