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: Birkhäuser, 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.


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