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On Analysis of Fractional Navier-Stokes Equations via Nonsingular Solutions and Approximation

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  • Emile Franc Doungmo Goufo
  • Stella Mugisha

Abstract

Until now, all the investigations on fractional or generalized Navier-Stokes equations have been done under some restrictions on the different values that can take the fractional order derivative parameter . In this paper, we analyze the existence and stability of nonsingular solutions to fractional Navier-Stokes equations of type ( ) defined below. In the case where , we show that the stability of the (quadratic) convergence, when exploiting Newton’s method, can only be ensured when the first guess is sufficiently near the solution . We provide interesting well-posedness and existence results for the fractional model in two other cases, namely, when and

Suggested Citation

  • Emile Franc Doungmo Goufo & Stella Mugisha, 2015. "On Analysis of Fractional Navier-Stokes Equations via Nonsingular Solutions and Approximation," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, July.
    • Handle: RePEc:hin:jnlmpe:212760
    DOI: 10.1155/2015/212760
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