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**Navier-Stokes equations. Theory and numerical analysis. Repr. with corr.
Repr. with corr.**
*(English)*
Zbl 0981.35001

Providence, RI: American Mathematical Society (AMS). xiv, 408 p. (2001).

This book is a new edition of previous versions [Navier-Stokes equations. Theory and numerical analysis (1977; Zbl 0383.35057), (1979; Zbl 0426.35003), and (1984; Zbl 0568.35002)] published by North-Holland. The first edition arose from classes taught by the author at the university of Maryland in 1972 and 1973. There has been a translation in Russian [(1981; Zbl 0529.35002)].

In the book under review, it is stated in the preface: “It has been decided to reproduce the book as it was in the last edition”. Appendix three however is an addition and it reproduces another publication of the author in [Jean-Paul Pier (ed.), Development of mathematics 1950-2000, Basel: BirkhĂ¤user, 1049-1106 (2000; Zbl 0970.35103)]. In this appendix there is an elaboration on the well-posedness of the incompressible Navier-Stokes equation, on turbulence and attractors, and one finds some comments on compressibility effects, numerical computations, and control. An extensive bibliography is attached to this addition.

In the book under review, it is stated in the preface: “It has been decided to reproduce the book as it was in the last edition”. Appendix three however is an addition and it reproduces another publication of the author in [Jean-Paul Pier (ed.), Development of mathematics 1950-2000, Basel: BirkhĂ¤user, 1049-1106 (2000; Zbl 0970.35103)]. In this appendix there is an elaboration on the well-posedness of the incompressible Navier-Stokes equation, on turbulence and attractors, and one finds some comments on compressibility effects, numerical computations, and control. An extensive bibliography is attached to this addition.

Reviewer: A.Akutowicz (Berlin)

### MathOverflow Questions:

Local strong solution to Navier-Stokes equation by Galerkin method without using the eigenfunctions of the Stokes operator### MSC:

35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

35Q30 | Navier-Stokes equations |

65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

35B40 | Asymptotic behavior of solutions to PDEs |