Book Review
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MathSciNet review:
1567880
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Book Information:
Authors:
Heinz-Otto Kreiss and
Jens Lorenz
Title:
Initial-boundary value problems and the Navier-Stokes equations
Additional book information:
Academic Press, New York, 1989, 398 pp., $54.50. ISBN 0-12-426125-6.
L. Caffarelli, R. Kohn, and L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 35 (1982), no. 6, 771–831. MR 673830, DOI 10.1002/cpa.3160350604
[CLMS] R. Coifman, P. -L. Lions, Y. Meyer, and S. Semmes, Compensated compactness and Hardy spaces, C. R. Acad. Sci. Paris (to appear).
Peter Constantin, Note on loss of regularity for solutions of the $3$-D incompressible Euler and related equations, Comm. Math. Phys. 104 (1986), no. 2, 311–326. MR 836008
Peter Constantin, Navier-Stokes equations and area of interfaces, Comm. Math. Phys. 129 (1990), no. 2, 241–266. MR 1048693
P. Constantin, C. Foias, O. P. Manley, and R. Temam, Determining modes and fractal dimension of turbulent flows, J. Fluid Mech. 150 (1985), 427–440. MR 794051, DOI 10.1017/S0022112085000209
Peter Constantin and Ciprian Foias, Navier-Stokes equations, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1988. MR 972259
C. Foiaş, Statistical study of Navier-Stokes equations. I, II, Rend. Sem. Mat. Univ. Padova 48 (1972), 219–348 (1973); ibid. 49 (1973), 9–123. MR 352733
C. Foiaş and R. Temam, Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations, J. Math. Pures Appl. (9) 58 (1979), no. 3, 339–368. MR 544257
Ciprian Foiaş, Colette Guillopé, and Roger Temam, New a priori estimates for Navier-Stokes equations in dimension $3$, Comm. Partial Differential Equations 6 (1981), no. 3, 329–359. MR 607552, DOI 10.1080/03605308108820180
Yoshikazu Giga and Tetsuro Miyakawa, Navier-Stokes flow in $\mathbf R^3$ with measures as initial vorticity and Morrey spaces, Comm. Partial Differential Equations 14 (1989), no. 5, 577–618. MR 993821, DOI 10.1080/03605308908820621
Eberhard Hopf, Statistical hydromechanics and functional calculus, J. Rational Mech. Anal. 1 (1952), 87–123. MR 59119, DOI 10.1512/iumj.1952.1.51004
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
Sergiu Klainerman and Andrew Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math. 34 (1981), no. 4, 481–524. MR 615627, DOI 10.1002/cpa.3160340405
Jean Leray, Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math. 63 (1934), no. 1, 193–248 (French). MR 1555394, DOI 10.1007/BF02547354
[L-L] L. Landau and E. Lifschitz, Fluid mechanics, Addison-Wesley, New York, 1953.
A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Applied Mathematical Sciences, vol. 53, Springer-Verlag, New York, 1984. MR 748308, DOI 10.1007/978-1-4612-1116-7
Ronald J. DiPerna and Andrew J. Majda, Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys. 108 (1987), no. 4, 667–689. MR 877643
David Ruelle, Large volume limit of the distribution of characteristic exponents in turbulence, Comm. Math. Phys. 87 (1982/83), no. 2, 287–302. MR 684105
James Serrin, The initial value problem for the Navier-Stokes equations, Nonlinear Problems (Proc. Sympos., Madison, Wis., 1962) Univ. Wisconsin Press, Madison, Wis., 1963, pp. 69–98. MR 0150444
Roger Temam, Navier-Stokes equations. Theory and numerical analysis, Studies in Mathematics and its Applications, Vol. 2, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. MR 0609732
[VF] M. J. Vishik and A. V. Fursikov, Mathematical problems of statistical hydromechanics, Kluwer Acad. Publ., Dordrecht, Holland, 1988.
Wolf von Wahl, The equations of Navier-Stokes and abstract parabolic equations, Aspects of Mathematics, E8, Friedr. Vieweg & Sohn, Braunschweig, 1985. MR 832442, DOI 10.1007/978-3-663-13911-9
V. I. Judovič, Non-stationary flows of an ideal incompressible fluid, Ž. Vyčisl. Mat i Mat. Fiz. 3 (1963), 1032–1066 (Russian). MR 158189
- [CKN] L. Caffarelli, R. Kohn, and L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 35 (1982), 771-831. MR 0673830
- [CLMS] R. Coifman, P. -L. Lions, Y. Meyer, and S. Semmes, Compensated compactness and Hardy spaces, C. R. Acad. Sci. Paris (to appear).
- [C1] P. Constantin, Note on loss of regularity for solutions of the 3-D incompressible Euler and related equations, Comm. Math. Phys. 104 (1986), 311-326. MR 836008
- [C2] P. Constantin, Navier-Stokes equations and area of interfaces, Comm. Math. Phys. (to appear). MR 1048693
- [CFMT] P. Constantin, C. Foias, O. Manley, and R. Temam, Determining modes and fractal dimension of turbulent flows, J. Fluid Mech. 150 (1985), 427-440. MR 794051
- [CF] P. Constantin and C. Foias, Navier-Stokes equations, The Univ. of Chicago Press, Chicago, 1988. MR 972259
- [F] C. Foias, Statistical study of Navier-Stokes equations, I, Rend. Sem. Mat. Univ. Padova 48 (1973), 219-349. MR 352733
- [FT] C. Foias and R. Temam, Some analytic and geometric properties of the solutions of the Navier-Stokes equations, J. Math. Pures Appl. 58 (1979), 339-368. MR 544257
- [FGT] C. Foias, C. Guillope, and R. Temam, New a priori estimates for Navier-Stokes equations in dimension 3, Comm. Partial Differential Equations 6 (1981), 329-359. MR 607552
- [GM] Y. Giga and T. Miyakawa, Navier-Stokes flow in R3 with measures as initial vorticity and Morrey spaces, Comm. Partial Differential Equations 14 (1989), 577-618. MR 993821
- [H] E. Hopf, Statistical hydrodynamics and functional calculus, J. Rat. Mech. Anal. 1 (1952), 87-123. MR 59119
- [K] T. Kato, Non-stationary flows of viscous and ideal fluids in R3, J. Funct. Anal. 9 (1972), 296-305. MR 481652
- [KM] S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math. 34 (1981), 481-524. MR 615627
- [L] J. Leray, Sur le mouvement d'un liquide viqueux emplissant l'espace, Acta Math. 63 (1934), 193-248. MR 1555394
- [L-L] L. Landau and E. Lifschitz, Fluid mechanics, Addison-Wesley, New York, 1953.
- [M] A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Appl. Math. Sci., vol. 53, Springer-Verlag, New York, 1984. MR 748308
- [M-dP] A. Majda and R. DiPerna, Oscillations and concentrations in weak solutions of the incompressible fluid equations, Comm. Math. Phys. 108 (1987), 667-689. MR 877643
- [R.] D. Ruelle, Large volume limit of distributions of characteristic exponents in turbulence, Comm. Math. Phys. 87 (1982), 287-302. MR 684105
- [S] J. Serrin, The initial value problem for the Navier-Stokes equations, Nonlinear Problems (R. E. Langer, ed.), Univ. of Wisconsin Press, Madison, 1963. MR 150444
- [T] R. Temam, Navier-Stokes equations, North-Holland, Amsterdam, 1977. MR 609732
- [VF] M. J. Vishik and A. V. Fursikov, Mathematical problems of statistical hydromechanics, Kluwer Acad. Publ., Dordrecht, Holland, 1988.
- [vW] W. von Wahl, The equations of Navier-Stokes and abstract parabolic equations, Vieweg and Sohn, Braunschweig and Wiesbaden, 1988. MR 832442
- [Y] V. I. Yudovitch, Non-stationary flow of an ideal incompressible liquid, Zh. Vychisl. Mat. i Mat. Fiz. 3 (1963), 1032-1066. MR 158189
Review Information:
Reviewer:
Peter Constantin
Journal:
Bull. Amer. Math. Soc.
23 (1990), 555-559
DOI:
https://doi.org/10.1090/S0273-0979-1990-15979-8