Determination of the solutions of the NavierStokes equations by a set of nodal values
Abstract
The NavierStokes equations of a viscous incompressible fluid and extent to which their solutions can be determined by a discrete set of nodal values of these solutions are investigated. The results presented are exact results and not approximate ones: it is shown 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. Two typical results are the following ones: two stationary solutions coincide if they coincide on a set sufficiently dense but finite; similarly if the largetime behavior of the solutions to the NavierStokes equations is known on an appropriate discrete set, then the largetime behavior of the solution itself is totally determined.
 Publication:

Mathematics of Computation
 Pub Date:
 July 1984
 Bibcode:
 1984MaCom..43..117F
 Keywords:

 Computational Fluid Dynamics;
 NavierStokes Equation;
 Set Theory;
 Turbulent Flow;
 Discrete Functions;
 Flow Velocity;
 Oscillating Flow;
 Points (Mathematics);
 Steady Flow;
 Stokes Flow;
 Strange Attractors;
 Time Dependence;
 Fluid Mechanics and Heat Transfer