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

• Main Authors: Emile Franc Doungmo Goufo, Stella Mugisha
• Format: Article
• Language: English
• Published: Hindawi Limited 2015-01-01
• Series: Mathematical Problems in Engineering
• Online Access: http://dx.doi.org/10.1155/2015/212760

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 β. In this paper, we analyze the existence and stability of nonsingular solutions to fractional Navier-Stokes equations of type (ut+u·∇u+∇p-Re-1(-∇)βu=f  in  Ω×(0,T]) defined below. In the case where β=2, we show that the stability of the (quadratic) convergence, when exploiting Newton’s method, can only be ensured when the first guess U0 is sufficiently near the solution U. We provide interesting well-posedness and existence results for the fractional model in two other cases, namely, when 1/2<β<1 and β≥1/2+(3/4).