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Existence and approximations of solutions for time‐fractional Navier‐stokes equations
Author(s) -
Peng Li,
Debbouche Amar,
Zhou Yong
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4779
Subject(s) - mathematics , uniqueness , convergence (economics) , work (physics) , mathematical analysis , fractional calculus , approximations of π , navier–stokes equations , derivative (finance) , galerkin method , finite element method , mechanical engineering , physics , aerospace engineering , compressibility , financial economics , engineering , economics , thermodynamics , economic growth
The purpose of this work is to investigate the problem of solutions to the time‐fractional Navier‐Stokes equations with Caputo derivative operators. We obtain the existence and uniqueness of the solutions to each approximate equation, as well as the convergence of the approximate solutions. Furthermore, we present some convergence results for the Faedo‐Galerkin approximations of the given problems.