Foiaş, Ciprian; Temam, Roger Determination of the solutions of the Navier-Stokes equations by a set of nodal values. (English) Zbl 0563.35058 Math. Comput. 43, 117-133 (1984). The authors give several very interesting results on the determination of the solutions of the Navier-Stokes equations of incompressible viscous fluids by their values on a finite set. For instance, two stationary solutions in a bounded domain \(\Omega\) of \({\mathbb{R}}^ n\), \(n=2,3\) coincide if they coincide on a finite set sufficiently dense. In the 2-dimensional case, let f,g be two body forces such that f(t)- g(t)\(\to 0\) in \(L^ 2\), as \(t\to +\infty\). Then if the corresponding strong solutions u and v are such that \(u(x_ j,t)-v(x_ j,t)\to 0\) in \(L^ 2\) as \(t\to \infty\), for every \(x_ j\) of a finite set, sufficiently dense, then u(\(\cdot,t)-v(\cdot,t)\to 0\) in C(\({\bar \Omega}\)). A similar statement holds for time-periodic solutions. The large time behaviour of the solution is therefore determined by its large time behaviour on a suitable discrete set. Reviewer: J.-C.Saut Cited in 3 ReviewsCited in 71 Documents MSC: 35Q30 Navier-Stokes equations 35B40 Asymptotic behavior of solutions to PDEs 35B60 Continuation and prolongation of solutions to PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:nodal values; Navier-Stokes equations; incompressible viscous fluids; stationary solutions; large time behaviour PDFBibTeX XMLCite \textit{C. Foiaş} and \textit{R. Temam}, Math. Comput. 43, 117--133 (1984; Zbl 0563.35058) Full Text: DOI