| Title:
|
Local and global existence and behaviour for $t\to \infty$ of solutions of the Navier-Stokes equations (English) |
| Author:
|
von Wahl, Wolf |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
26 |
| Issue:
|
1 |
| Year:
|
1985 |
| Pages:
|
151-167 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34G20 |
| MSC:
|
35A05 |
| MSC:
|
35B40 |
| MSC:
|
35Q10 |
| MSC:
|
35Q30 |
| MSC:
|
35R20 |
| idZBL:
|
Zbl 0575.35074 |
| idMR:
|
MR797298 |
| . |
| Date available:
|
2008-06-05T21:20:29Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106352 |
| . |
| Reference:
|
[FK] Fujita H., Kato T.: On the Navier-Stokes initial value problem I.Arch. Rat. Mech. Anal. 16, 269-315 (1964). Zbl 0126.42301, MR 0166499 |
| Reference:
|
[FM] Fujiwara D., Morimoto H.: An $L_r$-theorem of the Helmholtz decomposition of vector fields.J. Fac. Sci. Univ. Tokyo, Sect. IA Math. 24, 685-700 (1977). Zbl 0386.35038, MR 0492980 |
| Reference:
|
[Gi1] Giga Y.: Analyticity of the Semigroup Generated by the Stokes Operator in $L_r$-Spaces.Math. Z. 178, 297-329 (1981). Zbl 0473.35064, MR 0635201 |
| Reference:
|
[Gi2] Giga Y.: Domains in $L_r$-spaces of fractional powers of the Stokes operator.to appear in Archive Rat. Mech. Anal. |
| Reference:
|
[GiЗ] Giga Y.: Regularity criteria for weak solutions of the Navier-Stokes system.Preprint. Zbl 0598.35094, MR 0843578 |
| Reference:
|
[K] Kato T.: Nonlinear evolution equations in Banach spaces.Proc. Symp. Appl. Math. 17, 50-67, New York: American Mathematical Society 1965. Zbl 0173.17104, MR 0184099 |
| Reference:
|
[La] Ladyzhenskaja O.A.: The Mathematical Theory of Viscous Incompressible Flow.New York, London, Paris: Gordon and Breach 1969. MR 0254401 |
| Reference:
|
[L] Lions J. L.: Quelques méthodes de résolution des problémes aux limites non linéaires.Paris: Dunod 1969. Zbl 0189.40603, MR 0259693 |
| Reference:
|
[M] Masuda K.: On the stability of incompressible viscous fluid motions past objects.J. Math. Soc. Japan 27, 294-327 (1975). Zbl 0303.76011, MR 0440224 |
| Reference:
|
[S] Serrin J.: The initial value problem for the Navier-Stokes equations.Nonlinear Problems (R. Langer ed.), 69-98, Madison: The University of Wisconsin press 1963. Zbl 0115.08502, MR 0150444 |
| Reference:
|
[So] Sohr H.: Zur Regularitätstheorie der instationären Gleichungen von Navier-Stokes.Math. Z. 184, 359-376 (1983). Zbl 0506.35084, MR 0716283 |
| Reference:
|
[Sol] Solonnikov V. A.: Estimates for solutions of nonstationary Navier-Stokes equations.J. Soviet Math. 8, 467-529 (1977). Zbl 0404.35081 |
| Reference:
|
[SW] Sohr H., Wahl W. von: On the Singular Set and the Uniqueness of Weak Solutions of the Navier-Stokes Equations.Sonderforschungsbereich 72 "Approximation und Optimierung", Universität Bonn. Preprint no. 635 (1984). MR 0762786 |
| Reference:
|
[W1] Wahl W. von: Über das Verhalten für $t \rightarrow 0$ der Lösungen nichtlinearer parabolischer Gleichungen, insbesondere der Gleichungen von Navier-Stokes.Sonderforschungsbereich 72 "Approximation und Optiraierung", Universität Bonn. Preprint no. 602 (1983). Berichtigung hierzu. Sonderforschungsbereich 72 "Approxirmation und Optimierung", Universität Bonn. Preprint-Reihe (1983). MR 0742689 |
| Reference:
|
[W2] Wahl W. von: Regularity Questions for the Navier-Stokes Equations. Approximation Methods for Navier-Stokes Problems.Proceedings, Paderborn, Germany 1979. Lecture Notes in Mathematics 771 (1900). MR 0566019 |
| Reference:
|
[WЗ] Wahl W. von: Regularitätsfragen für die instationären Navier-Stokesschen Gleichungen in höheren Dimensionen.J. Math. Soc. Japan 32, 263-283 (1980). MR 0567419 |
| Reference:
|
[W4] Wahl W. von: Regularity of Weak Solutions of the Navier-Stokes Equations.To appear in the Proceedings of the 1983 AMS Summer Institute on Nonlinear Functional Analysis and Applications. Proceedings of Symposia in Pure Mathematics. Am. Math. Soc.: Providence, Rhode Island. MR 0843635 |
| . |
