Existence and approximations of solutions for time-fractional Navier-Stokes equations. (English) Zbl 1406.35474
Summary: 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.
MSC:
| 35R11 | Fractional partial differential equations |
| 35Q30 | Navier-Stokes equations |
| 33E12 | Mittag-Leffler functions and generalizations |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
Faedo-Galerkin approximations; mild solutions; Mittag-Leffler functions; time-fractional Navier-Stokes equationsReferences:
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