Book Review
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MathSciNet review:
1568175
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Book Information:
Author:
Carlo Marchioro and Mario Pulvirenti
Title:
Mathematical theory of incompressible viscous fluids
Additional book information:
Applied Mathematical Sciences, vol. 96, Springer-Verlag, Berlin and New York, 1994, xi+283 pp. US$49.00. ISBN 0-387-94044-8.
[1] V. I. Yudovitch, Non-stationary flow of an ideal incompressible liquid, Zh. Vychisl. Mat. i Mat. Fiz. 3 (1966), 1032.
Norman J. Zabusky, M. H. Hughes, and K. V. Roberts, Contour dynamics for the Euler equations in two dimensions, J. Comput. Phys. 30 (1979), no. 1, 96–106. MR 524163, DOI 10.1016/0021-9991(79)90089-5
Alexandre Joel Chorin, The evolution of a turbulent vortex, Comm. Math. Phys. 83 (1982), no. 4, 517–535. MR 649815
Andrew Majda, Vorticity and the mathematical theory of incompressible fluid flow, Comm. Pure Appl. Math. 39 (1986), no. S, suppl., S187–S220. Frontiers of the mathematical sciences: 1985 (New York, 1985). MR 861488, DOI 10.1002/cpa.3160390711
Jean-Yves Chemin, Persistance de structures géométriques dans les fluides incompressibles bidimensionnels, Ann. Sci. École Norm. Sup. (4) 26 (1993), no. 4, 517–542 (French, with English and French summaries). MR 1235440
A. L. Bertozzi and P. Constantin, Global regularity for vortex patches, Comm. Math. Phys. 152 (1993), no. 1, 19–28. MR 1207667
Peter Constantin, Geometric and analytic studies in turbulence, Trends and perspectives in applied mathematics, Appl. Math. Sci., vol. 100, Springer, New York, 1994, pp. 21–54. MR 1277191, DOI 10.1007/978-1-4612-0859-4_{2}
Peter Constantin and Charles Fefferman, Direction of vorticity and the problem of global regularity for the Navier-Stokes equations, Indiana Univ. Math. J. 42 (1993), no. 3, 775–789. MR 1254117, DOI 10.1512/iumj.1993.42.42034
Tosio Kato, Nonstationary flows of viscous and ideal fluids in $\textbf {R}^{3}$, J. Functional Analysis 9 (1972), 296–305. MR 0481652, DOI 10.1016/0022-1236(72)90003-1
- [1]
- V. I. Yudovitch, Non-stationary flow of an ideal incompressible liquid, Zh. Vychisl. Mat. i Mat. Fiz. 3 (1966), 1032.
- [2]
- N. Zabusky, M. H. Hughes, and K. V. Roberts, Contour dynamics for the Euler equations in two dimensions, J. Comput. Phys. 30 (1979), 96-106. MR 524163 (80g:76016)
- [3]
- A. J. Chorin, The evolution of a turbulent vortex, Comm. Math. Phys. 83 (1982), 517. MR 649815 (83g:76042)
- [4]
- M. Majda, Vorticity and the mathematical theory of incompressible fluid flow, Comm. Pure Appl. Math. 39 (1986), 187-220. MR 861488 (87j:76041)
- [5]
- J.-Y. Chemin, Persistence de structures geometriques dans les fluides incompressibles bidimensionnels, Ann. Sci. École Norm. Sup. (4) (to appear). MR 1235440 (94j:35141)
- [6]
- A. Bertozzi and P. Constantin, Global regularity for vortex patches, Comm. Math. Phys. 152 (1993), 19-28. MR 1207667 (94b:35221)
- [7]
- P. Constantin, Geometric and analytic studies in turbulences, Trends and Perspectives in Appl. Math. (L. Sirovich, ed.) Appl. Math. Sci., vol. 100, Springer, New York, 1994. MR 1277191 (95f:76017)
- [8]
- P. Constantin and Ch. Fefferman, Direction of vorticity and the problem of global regularity for the Navier-Stokes equation, Indiana Univ. Math. J. 42 (1993), 775. MR 1254117 (95j:35169)
- [9]
- T. Kato, Nonstationary flows of viscous and ideal fluids in R3, J. Funct. Anal. 9 (1972), 296. MR 0481652 (58:1753)
Review Information:
Reviewer:
Peter Constantin
Journal:
Bull. Amer. Math. Soc.
32 (1995), 288-290
DOI:
https://doi.org/10.1090/S0273-0979-1995-00582-3
