✍ Scribed by Werner Varnhorn
No coin nor oath required. For personal study only.
In the present paper we use a time delay ϵ > 0 for an energy conserving approximation of the non‐linear term of the non‐stationary Navier–Stokes equations. We prove that the corresponding initial‐value problem (N~ϵ~) in smoothly bounded domains G ⊆ ℝ^3^ is well‐posed. We study a semidiscretized difference scheme for (N~ϵ~) and prove convergence to optimal order in the Sobolev space H^2^(G). Passing to the limit ϵ→0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier–Stokes problem (N~o~) in a weak sense (Hopf).
📜 SIMILAR VOLUMES
## Abstract We consider first and second‐order implicit time stepping procedures for the non‐stationary Stokes equations in bounded domains of ℝ^3^. Using energy estimates we prove the optimal convergence properties in the Sobolev spaces __H__^__m__^(G)(m = 0, 1, 2) uniformly in time, provided that
## Abstract A new formulation of the Navier–Stokes equations is introduced to solve incompressible flow problems. When finite element methods are used under this formulation there is no need to worry whether Babuska–Brezzi condition is satisfied or not. Both velocity and pressure can be obtained se
## Abstract The local existence, uniqueness and regularity of solutions of the initial‐value problem for non‐stationary Navier–Stokes equations are studied via abstract Besov spaces. The assumptions about Ω the initial data and the external force are improved on by rather simple proofs.