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Title: On evolution inequalities of a modified Navier-Stokes type. I (English)
Author: Müller, Manfred
Author: Naumann, Joachim
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 23
Issue: 3
Year: 1978
Pages: 174-184
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: The paper present an existence theorem for a strong solution to an abstract evolution inequality where the properties of the operators involved are motivated by a type of modified Navier-Stokes equations under certain unilateral boundary conditions. The method of proof rests upon a Galerkin type argument combined with the regularization of the functional. (English)
Keyword: existence and regularity of solutions
Keyword: boundary value problems
Keyword: viscous incompressible fluid
Keyword: modified Navier-Stokes equations
Keyword: evolution inequalities
Keyword: Faedo-Galerkin approximation
MSC: 35Q10
MSC: 35Q30
MSC: 35R20
MSC: 47H15
MSC: 49J40
idZBL: Zbl 0424.35072
idMR: MR0482433
DOI: 10.21136/AM.1978.103743
Date available: 2008-05-20T18:09:24Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] Biroli M.: Sur l'inéquation d'évolution de Navier-Stokes.Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat., (8) 52 (1972); Nota I: 457-459; Nota II: 591-598; Nota III: 811-820. Zbl 0249.35073, MR 0399675
Reference: [2] Biroli M.: Sur la solution faible des inéquations d'évolution du type de Navier-Stokes avec convexe dépendant du temps.Boll. U. M. I., (4) 11 (1975), 309-321. Zbl 0307.35074, MR 0420034
Reference: [3] Brézis H.: Inéquations variationnelles relatives à l'opérateur de Navier-Stokes.J. Math. Anal. Appl., 39 (1972), 159-165. Zbl 0238.35068, MR 0312349, 10.1016/0022-247X(72)90231-4
Reference: [4] Brézis H.: Opérateurs maximaux monotones et semigroupes de contractions dans les escapes de Hilbert.Math. Studies 5, North Holland, 1973.
Reference: [5] Ladyshenskaja O. A.: On new equations for describing the motion of viscous, incompressible fluids and the global solvability of their boundary value problems.(Russian). Trudy Mat. Inst. Akad. Nauk SSSR, СII (1967), 85-104.
Reference: [6] Ladyshenskaja O. A.: On modifications of the Navier-Stokes equations with big gradient of velocity.(Russian). Zap. Nauch. Sem. Leningr. Ot. Mat. Inst., 7 (1968), 126-154. MR 0241832
Reference: [7] Lions J. L.: Quelques méthodes de résolution des problèmes aux limites non linéaires.Paris 1969. Zbl 0189.40603, MR 0259693
Reference: [8] Prouse G.: On a unilateral problem for the Navier-Stokes equations.Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat., (8) 62 (1972); Nota I: 337-342; Nota II: 467-478. Zbl 0253.35067, MR 0342882
Reference: [9] Yosida K.: Functional analysis.Berlin, Göttingen, Heidelberg 1965. Zbl 0126.11504, MR 0180824


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