Bulletin of the American Mathematical Society

MathSciNet review: 1567027
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Daniel D. Joseph
Title: Stability of fluid motions.
Additional book information: Springer Tracts in Natural Philosophy, vol. 28, Springer-Verlag, New York, 1976, xiii + 282 pp., $39.80, and xiv + 274 pp., $39.80.

E. Hopf, Abzweigung einer periodischen Lösung eines Differential systems. Berichte Math.-Phys. Kl. Sächsischen Akad. Wiss. Leipzig, XCIV, 1942, 1-22.

G. Iooss, Theorie non linéaire de la stabilité des ecoulements laminaires dans le cas de “L’ Exchange des Stabilités”, Arch. Rational Mech. Anal. 40 (1971), 166-208.

Daniel D. Joseph, Stability of convection in containers of arbitrary shape, J. Fluid Mech. 47 (1971), 257–282. MR 307582, DOI 10.1017/S0022112071001046

D. D. Joseph and D. H. Sattinger, Bifurcating time periodic solutions and their stability, Arch. Rational Mech. Anal. 45 (1972), 79–109. MR 387844, DOI 10.1007/BF00253039

K. Kirchgässner and P. Sorger, Stability analysis of branching solutions of the Navier-Stokes equations, Applied mechanics (Proc. Twelfth Internat. Congr. Appl. Mech., Stanford Univ., Stanford, Calif., 1968) Springer, Berlin, 1969, pp. 257–268. MR 0375929

L. Landau, On the problem of turbulence, C. R. (Doklady) Acad. Sci. URSS (N.S.) 44 (1944), 311–314. MR 0011997

E. Palm, On the tendency towards hexagonal cells in steady convection, J. Fluid Mech. 8 (1960), 183-192.

Giovanni Prodi, Teoremi di tipo locale per il sistema di Navier-Stokes e stabilità delle soluzioni stazionarie, Rend. Sem. Mat. Univ. Padova 32 (1962), 374–397 (Italian). MR 189354

O. Reynolds, An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philos. Trans. Roy. Soc. London Ser. A 174 (1883), 935-982.

D. H. Sattinger, The mathematical problem of hydrodynamic stability, J. Math. Mech. 19 (1969/1970), 979–817. MR 0261182

D. H. Sattinger, Bifurcation of periodic solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 41 (1971), 66–80. MR 272257, DOI 10.1007/BF00250178

James Serrin, On the stability of viscous fluid motions, Arch. Rational Mech. Anal. 3 (1959), 1–13. MR 105250, DOI 10.1007/BF00284160

J. T. Stuart, On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. I. The basic behaviour in plane Poiseuille flow, J. Fluid Mech. 9 (1960), 353–370. MR 128228, DOI 10.1017/S002211206000116X

V. I. Iudovich, The onset of auto-oscillations in a fluid, Prikl. Mat. Meh. 35 (1971), 638–655 (Russian); English transl., J. Appl. Math. Mech. 35 (1971), 587–603 (1972). MR 0381502, DOI 10.1016/0021-8928(71)90053-0

E. Hopf, Abzweigung einer periodischen Lösung eines Differential systems. Berichte Math.-Phys. Kl. Sächsischen Akad. Wiss. Leipzig, XCIV, 1942, 1-22.




G. Iooss, Theorie non linéaire de la stabilité des ecoulements laminaires dans le cas de “L’ Exchange des Stabilités”, Arch. Rational Mech. Anal. 40 (1971), 166-208.




D. D. Joseph, Stability of convection in containers of arbitrary shape, J. Fluid Mech. 47 (1971), 257-282. MR 0307582




D. D. Joseph and D. H. Sattinger, Bifurcating time periodic solutions and their stability, Arch. Rational Mech. Anal. 45 (1972), 79-109. MR 387844




K. Kirchgässner and P. Sorger, Stability analysis of branching solutions of the Navier-Stokes equations, Proc. 12th Internat. Congress Appl. Math., Stanford, 1968, pp. 257-268. MR 375929




L. Landau, On the problem of turbulence, C. R. Acad. Sci. U.S.S.R. 44 (1944), 311-314. MR 11997




E. Palm, On the tendency towards hexagonal cells in steady convection, J. Fluid Mech. 8 (1960), 183-192.




G. Prodi, Teoremi di tipo locale per il sistema di Navier-Stokes e stabilita delle soluzioni stazionarie, Rend. Sem. Univ. Padova 32 (1962), 374-397. MR 189354




O. Reynolds, An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philos. Trans. Roy. Soc. London Ser. A 174 (1883), 935-982.




D. H. Sattinger, The mathematical problem of hydrodynamic stability, J. Math. Mech. 19 (1970), 797-817. MR 261182




D. H. Sattinger, Bifurcation of periodic solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 41 (1971), 66-80. MR 272257




J. Serrin, On the stability of viscous fluid motions, Arch. Rational Mech. Anal. 3 (1959), 1-13. MR 105250




J. T. Stuart, On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows. Part 1: The basic behaviour in plane Poiseuille flow, J. Fluid Mech. 9 (1960), 353-370. MR 128228




V. I. Yudovich, The onset of auto-oscillations in a viscous fluid, J. Appl. Math. Mech. 35 (1971), 638-655. MR 381502