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A variational approach for the vector potential formulation of the Stokes and Navier-Stokes problems in three dimensional domains. (English) Zbl 0591.35053
Using the Georgescu’s results on Hodge-Kodaira decomposition [V. Georgescu, Ann. Mat. Pura Appl., IV. Ser. 122, 159-198 (1979; Zbl 0432.58026)] a vorticity-vector potential formulation of the Stokes problem in three-dimensional simply connected domain is obtained. The usual boundary condition of vector-potential are imposed, and the divergence-free condition results. In the last part, the previous considerations are extended to the nonlinear Navier-Stokes system.
Reviewer: G.Pasa

35Q30 Navier-Stokes equations
35D05 Existence of generalized solutions of PDE (MSC2000)
Full Text: DOI
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