Statistical solutions of the Navier{endash}Stokes equations on the phase space of vorticity and the inviscid limits
- 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, Vol. 38, Issue 6; Other Information: PBD: Jun 1997
- Country of Publication:
- United States
- Language:
- English
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