For ν∈(0,1), we analyze the system of equations on the two dimensional domain Ω in the unknown function u=(u1(x,t),u2(x,t))ut−μΔu−γΔ∂t νu+u⋅∇u=−∇p+f,divu=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.
A subdiffusive Navier-Stokes-Voigt system
V. Pata;
2020-01-01
Abstract
For ν∈(0,1), we analyze the system of equations on the two dimensional domain Ω in the unknown function u=(u1(x,t),u2(x,t))ut−μΔu−γΔ∂t νu+u⋅∇u=−∇p+f,divu=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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
