A subdiffusive Navier-Stokes-Voigt system
| Autor: | Sergii V. Siryk, Nataliya Vasylyeva, Mykola Krasnoschok, Vittorino Pata |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Statistical and Nonlinear Physics Function (mathematics) Condensed Matter Physics System of linear equations 01 natural sciences Domain (mathematical analysis) 010305 fluids & plasmas Fractional calculus 0103 physical sciences Order (group theory) Uniqueness Limit (mathematics) 010306 general physics U-1 Mathematical physics |
| Popis: | For ν ∈ ( 0 , 1 ) , we analyze the system of equations on the two dimensional domain Ω in the unknown function u = ( u 1 ( x , t ) , u 2 ( x , t ) ) u t − μ Δ u − γ Δ ∂ t ν u + u ⋅ ∇ u = − ∇ p + f , div u = 0 , where ∂ t ν denotes the Riemann–Liouville fractional derivative of order ν . Under suitable conditions on the given data, the global existence and uniqueness of strong solutions to the related initial–boundary value problems are established for ν ∈ ( 0 , 1 ∕ 2 ) . The convergence of the strong solution to the one of the corresponding initial–boundary value problem to the Navier–Stokes equations is discussed, in the limit ν → 0 . We also present several numerical tests illustrating this convergence. |
| Databáze: | OpenAIRE |
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