Determination of the solutions of the Navier-Stokes equations by a set of nodal values

Author:

Foias Ciprian,Temam Roger

Abstract

We consider the Navier-Stokes equations of a viscous incompressible fluid, and we want to see to what extent these solutions can be determined by a discrete set of nodal values of these solutions. The results presented here are exact results and not approximate ones: we show, in several cases, that the solutions are entirely determined by their values on a discrete set, provided this set contains enough points and these points are sufficiently densely distributed (in a sense described in the article). Two typical results are the following ones: two stationary solutions coincide if they coincide on a set sufficiently dense but finite; similarly if the large time behavior of the solutions to the Navier-Stokes equations is known on an appropriate discrete set, then the large time behavior of the solution itself is totally determined.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference18 articles.

1. Pure and Applied Mathematics, Vol. 65;Adams, Robert A.,1975

2. Lecture Notes in Mathematics, Vol. 385;Douglas, Jim, Jr.,1974

3. Asymptotic analysis of the Navier-Stokes equations;Foias, C.;Phys. D,1983

4. Sur le comportement global des solutions non-stationnaires des équations de Navier-Stokes en dimension 2;Foiaş, C.;Rend. Sem. Mat. Univ. Padova,1967

5. Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations;Foiaş, C.;J. Math. Pures Appl. (9),1979

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