Robustness of regularity and convergence of Galerkin approximations for 3D generalized incompressible Navier-Stokes equations

Abstract

In this paper, we first consider the robustness of strong solutions for 3D generalized Navier- Stokes equations, i.e., we show the set of all initial conditions u₀ ∈ H¹(R³) with ∇·u₀ = 0 that give rise to a strong solution of the generalized Navier-Stokes equations on the time interval [0,T] is open inH¹(R³). Moreover, we prove that the Galerkin approximations of a strong solution of the 3D generalized Navier- Stokes equations converge strongly to u in L^∞(0,T;H¹_0,div(T³)) and L²(0,T;H^κ+1(T³) ∩ H¹_0,div(T³)).

Keywords

robustness / convergence / Galerkin approximations / strong solution / generalized Navier-Stokes equations

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