A specifically nonlinear property of the operator semigroup of the NavierStokes equations
Abstract
Foias (1974) and Foias and Temam (1975, 1979) have found that for the twodimensional NavierStokes equations the actual possible flows constitute very thin sets in the usual function phase space associated with the corresponding Cauchy problem. However, the same is true for the Stokes equations. The present investigation is concerned with a probabilistic property of thinness which is valid for the NavierStokes equations, but not for the Stokes equations. It is shown that for generic body forces the set of all possible flows at time t greater than zero is of null measure with respect to a large class of Gaussian measures on the function phase space, while for the Stokes equations this is not possible for any body force.
 Publication:

Communications in Pure Applied Mathematics
 Pub Date:
 March 1982
 Bibcode:
 1982CPAM...35..197F
 Keywords:

 Boundary Value Problems;
 Fluid Mechanics;
 Group Theory;
 NavierStokes Equation;
 Nonlinearity;
 Operators (Mathematics);
 Cauchy Problem;
 Flow Theory;
 Normal Density Functions;
 PhaseSpace Integral;
 Fluid Mechanics and Heat Transfer