Geodesic
On some way of the approximation of solutions of initial boundary value problems for Navier--Stokes equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 23, Tome 197 (1992), pp. 87-119

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Solutions of the initial boundary value problem for Navier–Stokes equations are approximated by solutions of the initial boundary value problem \begin{gather*} \partial_t u(t)+u_k(t)\partial_ku(t)-\nu\Delta u(t)-\frac1\varepsilon\nabla\mathrm{div}\,u(t)+\frac12u(t)\mathrm{div}\,u(t)=f(t),\\ u(0)=u_0\text{ in }\Omega;\quad u(t)=0\text{ on }\partial\Omega. \end{gather*} We study proximity of solutions of these problems in suitable norms and also proximity of their minimal global $B$-attractors. 
@article{ZNSL_1992_197_a4,
     author = {O. A. Ladyzhenskaya and G. A. Seregin},
     title = {On some way of the approximation of solutions of initial boundary value problems for {Navier--Stokes} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {87--119},
     publisher = {mathdoc},
     volume = {197},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_197_a4/}
}
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O. A. Ladyzhenskaya; G. A. Seregin. On some way of the approximation of solutions of initial boundary value problems for Navier--Stokes equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 23, Tome 197 (1992), pp. 87-119. http://geodesic.mathdoc.fr/item/ZNSL_1992_197_a4/