Translationally homogeneous statistical solutions and individual solutions with infinite energy of a system of Navier-Stokes equations

1979 ◽  
Vol 19 (5) ◽  
pp. 710-729 ◽  
Author(s):  
M. I. Vishik ◽  
A. V. Fursikov
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Infinite Energy ◽  
Statistical Solutions

A simple proof of existence of weak and statistical solutions of Navier–Stokes equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 1-11 ◽  
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Natural Number ◽  
Simple Proof ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence Proofs ◽  
Statistical Solutions

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.

Sign in / Sign up

Export Citation Format

Share Document