| 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:
|
http://hdl.handle.net/10338.dmlcz/103743 |
| . |
| 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 |
| . |
