A new formulation for the linearized Navier-Stokes equation

  • Abstract
  • Keywords
  • References
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  • Abstract

    This paper is devoted to study the Navier-Stokes equations by applying the curl and using a current function, weobtain a non-linear biharmonic problem where the pressure disappears and instead of the velocity, we are workingwith a scalar function. After a linearization, we obtain a sequence of linear problems. We study the existence anduniqueness of its solutions. Finally we show the convergence of the sequence of the linearized problems obtained tothe non-linear one.

    Keywords: Bi-Laplacian, Existence and uniqueness, Navier-Stokes equations.

  • References

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    2. Amara.M, Capatina-Papaghiuc.D, Chacon-Vera.E, Trijullo.D, "Vorticity velocity pressure formulation for Navier-Stokes equations", Comput. Vis. Sci, No.6, (2004), pp.47-52.
    3. Bernardi.C, Mady.Y, Rapetti.F, "Discretisations variationnelles de problmes aux limites elliptiques", Springer-Verlag Berlin Heidelberg, (2004).
    4. Girault.V, Raviart.P-A, "Finite Element Methods for the Navier-Stokes Equations, Theory and Algorithms", SpringerVerlag, (1986).
    5. Ndlec.J-C, "Cours d'Analyse Numrique", Ecole Nationale de Ponts et Chausses.
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Article ID: 3006
DOI: 10.14419/ijamr.v3i4.3006

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