zbMATH — the first resource for mathematics

Navier-Stokes equations. Theory and numerical analysis. 3rd (rev.) ed. (English) Zbl 0568.35002
Studies in Mathematics and its Applications, Vol. 2. Amsterdam-New York- Oxford: North-Holland. XII, 526 p. hbk: $ 84.50; Dfl. 220.00; pbk: $ 35.00; Dfl. 100.00 (1984).
[For the first two editions (1977 and 1979) see Zbl 0383.35057 and Zbl 0426.35003.]
This book enjoys a high esteem from the point of view of mathematical analysis as well as computational fluid dynamics. In this third revised edition the author supplemented the work by additional comments indicating recent progress in the following three directions: Existence, uniqueness and regularity of solutions; long time behavior and turbulence; Numerical approximation. The bibliography has been expanded appropriately. Compare also the author’s book ”Navier-Stokes equations and nonlinear functional analysis” [CBMS-NSF Reg. Conf. Ser. Appl. Math. 41 (1983; Zbl 0522.35002)].
Reviewer: H.Jeggle

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
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
35B40 Asymptotic behavior of solutions to PDEs