Equivalence of Invariant Measures and Stationary Statistical Solutions for The Autonomous Globally Modified Navier-Stokes Equations

By Peter E. Kloeden, Pedro Marín-Rubio, José Real. 2009

73 citations recorded by the source corpus.

A new proof of existence of solutions for the three dimensional system of globally modified Navier-Stokes equations introduced in [3] by Caraballo, Kloeden and Real is obtained using a smoother Galerkin scheme. This is then used to investigate the relationship between invariant measures and statistical solutions of this system in the case of temporally independent forcing term. Indeed, we are able to prove that a stationary statistical solution is also an invariant probability measure under suitable assumptions.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cd3b22615ddff28a882b2a753b0685055d489ae2

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Asymptotic regularity of trajectory attractor and trajectory statistical solution for the 3D globally modified Navier–Stokes equations (2019, background): “[4, 17]): u′(t) + νAu(t) +BN (u(t), u(t)) = g(t) in D′(0,+∞;V ′), (2.”
Three dimensional system of globally modified Navier-Stokesequations with infinite delays (2010, background): “The system (1) was introduced and studied in [1] (see also [2, 14, 15, 16, 3] and the review paper [13]).”