Remarks on the initial value problem for a stabilized NavierStokes equation
Abstract
A new family of simple, straightforward modifications of the NavierStokes equations is presented that can be made arbitrarily close to the original equations. These modifications possess the following properties: (1) the initial value problem for these 'stabilized' equations is appropriately stated and can be treated by the methods of Hopf, Prodi, Serrin, and Walter; (2) the proof of existence proposed by Hopf for the initial value problem in the NavierStokes equation leads to a constructive solution to the initial value problem in the stabilized equations. The NavierStokes equation is modified by averaging in the convective term. The classical and Hopf forms of the initial value problem are also briefly reviewed.
 Publication:

Gesellschaft angewandte Mathematik und Mechanik Jahrestagung Goettingen West Germany Zeitschrift Flugwissenschaften
 Pub Date:
 April 1975
 Bibcode:
 1975GMMWJ..55..218R
 Keywords:

 Boundary Value Problems;
 Existence Theorems;
 Fluid Mechanics;
 NavierStokes Equation;
 Numerical Stability;
 Convergence;
 Flow Equations;
 Fluid Mechanics and Heat Transfer