Statistical solutions of the Navier{endash}Stokes equations on the phase space of vorticity and the inviscid limits

Journal Article · Sun Jun 01 04:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532032· OSTI ID:503626

Constantin, P; Wu, J ^[1]

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1. Department of Mathematics, The University of Chicago, Chicago, Illinois 60637 (United States)

Using the methods of Foias [Sem. Math. Univ. Padova {bold 48}, 219{endash}343 (1972); {bold 49}, 9{endash}123 (1973)] and Vishik{endash}Fursikov [{ital Mathematical Problems of Statistical Hydromechanics} (Kluwer, Dordrecht, 1988)], we prove the existence and uniqueness of both spatial and space{endash}time statistical solutions of the Navier{endash}Stokes equations on the phase space of vorticity. Here the initial vorticity is in Yudovich space and the initial measure has finite mean enstrophy. We show under further assumptions on the initial vorticity that the statistical solutions of the Navier{endash}Stokes equations converge weakly and the inviscid limits are the corresponding statistical solutions of the Euler equations. {copyright} {ital 1997 American Institute of Physics.}

• DOE Contract Number: FG02-92ER25119
• OSTI ID: 503626
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 6 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CONVERGENCE
NAVIER-STOKES EQUATIONS
PHASE SPACE
STATISTICS
VORTICES