| Title:
|
Axisymmetric flow of Navier-Stokes fluid in the whole space with non-zero angular velocity component (English) |
| Author:
|
Neustupa, Jiří |
| Author:
|
Pokorný, Milan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
469-481 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study axisymmetric solutions to the Navier-Stokes equations in the whole three-dimensional space. We find conditions on the radial and angular components of the velocity field which are sufficient for proving the regularity of weak solutions. (English) |
| Keyword:
|
axisymmetric flow |
| Keyword:
|
Navier-Stokes equations |
| Keyword:
|
regularity of systems of PDE’s |
| MSC:
|
35B65 |
| MSC:
|
35D10 |
| MSC:
|
35J35 |
| MSC:
|
35Q30 |
| MSC:
|
35Q35 |
| MSC:
|
76D05 |
| idZBL:
|
Zbl 0981.35046 |
| idMR:
|
MR1844284 |
| DOI:
|
10.21136/MB.2001.134015 |
| . |
| Date available:
|
2009-09-24T21:52:54Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134015 |
| . |
| Reference:
|
[1] Galdi G. P.: An Introduction to the Navier-Stokes Initial Boundary Value Problem.Birhäuser Verlag, Topics in Mathematical Fluid Mechanics, Galdi G. P., Heywood J. G., Rannacher R. (eds.), to appear. Zbl 1108.35133, MR 1798753 |
| Reference:
|
[2] Giga Y.: Solutions for semilinear parabolic equations in $L^p$ and regularity of weak solutions of the Navier-Stokes equations.J. of Diff. Equations 61 (1986), 186–212. Zbl 0577.35058, MR 0833416, 10.1016/0022-0396(86)90096-3 |
| Reference:
|
[3] Kozono H.: Uniqueness and regularity of weak solutions to the Navier-Stokes equations.Lecture Notes Num. Appl. Anal vol. 16, 1998, pp. 161–208. Zbl 0941.35065, MR 1616331 |
| Reference:
|
[4] Kozono H., Sohr H.: Remark on uniqueness of weak solutions to the Navier-Stokes equations.Analysis 16 (1996), 255–271. MR 1403221, 10.1524/anly.1996.16.3.255 |
| Reference:
|
[5] Ladyzhenskaya O. A.: On the unique global solvability of the Cauchy problem for the Navier-Stokes equations in the presence of the axial symmetry.Zap. Nauch. Sem. LOMI 7 (1968), 155–177. (Russian) MR 0241833 |
| Reference:
|
[6] Leonardi S., Málek J., Nečas J., Pokorný M.: On axially symmetric flows in ${\mathbb{R}}^3$.Z. Anal. Anwend. 18 (1999), 639–649. MR 1718156, 10.4171/ZAA/903 |
| Reference:
|
[7] Leray J.: Sur le mouvements d’un liquide visqueux emplissant l’espace.Acta Math. 63 (1934), 193–248. MR 1555394, 10.1007/BF02547354 |
| Reference:
|
[8] Neustupa J., Novotný A., Penel P.: A remark to the interior regularity of a suitable weak solution to the Navier-Stokes equation.Preprint University of Toulon-Var (1999). |
| Reference:
|
[9] Neustupa J., Penel P.: Regularity of a suitable weak solution to the Navier-Stokes equations as a consequence of regularity of one velocity component.Plenum Press, Nonlinear Applied Analysis, A. Sequeira, H. Beirao da Veiga, J. Videman (eds.), 1999, pp. 391–402. MR 1727461 |
| Reference:
|
[10] Nirenberg L.: On elliptic partial differential equations.Ann. Scuola Norm. 13 (1959), 115–162. Zbl 0088.07601, MR 0109940 |
| Reference:
|
[11] Prodi G.: Un teorema di unicità per el equazioni di Navier-Stokes.Ann. Mat. Pura Appl. 48 (1959), 173–182. MR 0126088 |
| Reference:
|
[12] Serrin J.: The initial value problem for the Navier-Stokes equations.University of Wisconsin Press, Nonlinear Problems, R. E. Langer (ed.), 1963, pp. 69–98. Zbl 0115.08502, MR 0150444 |
| Reference:
|
[13] Sohr H., von Wahl W.: On the singular set and the uniqueness of weak solutions of the Navier-Stokes equations.Manuscripta Math. 49 (1984), 27–59. MR 0762786, 10.1007/BF01174870 |
| Reference:
|
[14] Uchovskii M. R., Yudovich B. I.: Axially symmetric flows of an ideal and viscous fluid.J. Appl. Math. Mech. 32 (1968), 52–61. MR 0239293, 10.1016/0021-8928(68)90147-0 |
| . |
