scholarly journals Statistical solutions of the Navier–Stokes equations on the phase space of vorticity and the inviscid limits

1997 ◽  
Vol 38 (6) ◽  
pp. 3031-3045 ◽  
Author(s):  
Peter Constantin ◽  
Jiahong Wu
Keyword(s):  
Phase Space ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
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.

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