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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.

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