Group classification of the two-dimensional Navier–Stokes-type equations

Manale, Jacob

doi:10.1016/s0020-7462(99)00046-3

Cited by 5 publications

(1 citation statement)

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“…Although existence and characterization of smooth or nonsingular solutions of NSEs have been comprehensively investigated in numerous works [2][3][4][5][6][7], they remain open problems. Fractional calculus applied to differential equations has captured a huge amount of attention recently [8][9][10][11][12] and it was shown that its applications lie in modeling many problems and phenomena in applied technology, engineering, and sciences including applied mathematics, computing, physics, biology, chemistry, economic, and other domains of applications.…”

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confidence: 99%

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

Goufo

Mugisha

2015

Mathematical Problems in Engineering

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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 parameterβ. 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 whereβ=2, we show that the stability of the (quadratic) convergence, when exploiting Newton’s method, can only be ensured when the first guessU0is sufficiently near the solutionU. We provide interesting well-posedness and existence results for the fractional model in two other cases, namely, when1/2<β<1andβ≥1/2+(3/4).

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