| Title:
|
On the motion of rigid bodies in a viscous fluid (English) |
| Author:
|
Feireisl, Eduard |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
47 |
| Issue:
|
6 |
| Year:
|
2002 |
| Pages:
|
463-484 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the problem of motion of several rigid bodies in a viscous fluid. Both compressible and incompressible fluids are studied. In both cases, the existence of globally defined weak solutions is established regardless possible collisions of two or more rigid objects. (English) |
| Keyword:
|
rigid body |
| Keyword:
|
compressible fluid |
| Keyword:
|
incompressible fluid |
| Keyword:
|
global existence |
| MSC:
|
35Q30 |
| MSC:
|
35Q35 |
| MSC:
|
76D03 |
| MSC:
|
76D05 |
| idZBL:
|
Zbl 1090.35137 |
| idMR:
|
MR1948192 |
| DOI:
|
10.1023/A:1023245704966 |
| . |
| Date available:
|
2009-09-22T18:11:31Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134509 |
| . |
| Reference:
|
[1] B. Desjardins, M. J. Esteban: Existence of weak solutions for the motion of rigid bodies in a viscous fluid.Arch. Rational Mech. Anal. 146 (1999), 59–71. MR 1682663, 10.1007/s002050050136 |
| Reference:
|
[2] B. Desjardins, M. J. Esteban: On weak solutions for fluid-rigid structure interaction: Compressible and incompressible models.Commun. Partial Differential Equations 25 (2000), 1399–1413. MR 1765138 |
| Reference:
|
[3] R. J. DiPerna and P.-L. Lions: Ordinary differential equations, transport theory and Sobolev spaces.Invent. Math. 98 (1989), 511–547. MR 1022305, 10.1007/BF01393835 |
| Reference:
|
[4] E. Feireisl: On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable.Comment. Math. Univ. Carolinae 42 (2001), 83–98. Zbl 1115.35096, MR 1825374 |
| Reference:
|
[5] E. Feireisl: On the motion of rigid bodies in a viscous compressible fluid.Arch. Rational Mech. Anal. (2002) (to appear). MR 1981859 |
| Reference:
|
[6] E. Feireisl: On the motion of rigid bodies in a viscous incompressible fluid.J. Evolution Equations (2002) (to appear). MR 2019028 |
| Reference:
|
[7] E. Feireisl, A. Novotný and H. Petzeltová: On the existence of globally defined weak solutions to the Navier-Stokes equations of compressible isentropic fluids.J. Math. Fluid Dynamics 3 (2001), 358–392. MR 1867887 |
| Reference:
|
[8] G. P. Galdi: On the steady self-propelled motion of a body in a viscous incompressible fluid.Arch. Rat. Mech. Anal. 148 (1999), 53–88. MR 1715453, 10.1007/s002050050156 |
| Reference:
|
[9] V. Giovangigli: Multicomponent Flow Modeling.Birkhäuser, Basel, 1999. Zbl 0956.76003, MR 1713516 |
| Reference:
|
[10] M. D. Gunzburger, H. C. Lee and A. Seregin: Global existence of weak solutions for viscous incompressible flow around a moving rigid body in three dimensions.J. Math. Fluid Mech. 2 (2000), 219–266. MR 1781915, 10.1007/PL00000954 |
| Reference:
|
[11] K.-H. Hoffmann, V. N. Starovoitov: Zur Bewegung einer Kugel in einer zäher Flüssigkeit.TUM-M9618, München, 1996. |
| Reference:
|
[12] P.-L. Lions: Mathematical Topics in Fluid Dynamics, Vol.2. Compressible models.Oxford Science Publication, Oxford, 1998. MR 1637634 |
| Reference:
|
[13] K. R. Rajagopal, L. Tao: Mechanics of Mixtures.World Scientific, Singapore, 1995. MR 1370661 |
| Reference:
|
[14] J. A. San Martin, V. Starovoitov and M. Tucsnak: Global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid.Arch. Rational Mech. Anal. 161 (2002), 93–112. MR 1870954 |
| Reference:
|
[15] D. Serre: Chute libre d’un solide dans un fluid visqueux incompressible. Existence.Jap. J. Appl. Math. 4 (1987), 99–110. MR 0899206, 10.1007/BF03167757 |
| Reference:
|
[16] G. G. Stokes: On the effect of internal friction of fluids on the motion of pendulums.Trans. Cambridge Phil. Soc. 9 (1851), 80–85. |
| . |
