## The Navier-Stokes equations. An elementary functional analytic approach.(English)Zbl 0983.35004

Birkhäuser Advanced Texts. Basel: Birkhäuser. x, 367 p. (2001).
The book is an elementary and selfcontained approach to the mathematical theory of viscous incompressible fluid in a completely general domain $$\Omega\subseteq \mathbb{R}^n$$ $$(n\geq 2)$$.
The monograph has five chapters. The first two chapters have an introductory character and contain, without proofs, some fundamental properties of spaces, distributions, operators, inequalities, embeddings, etc. In the third chapter, the stationary Navier-Stokes equations are investigated in the linearized and nonlinear cases, respectively. The nonstationary linearized theory is presented in chapter four, the full nonlinear case in chapter five.
The book is written in a well arranged way, easy to survey and with utilization of the newest results. For its study, it is necessary to know only the basic functional analytic tools in Hilbert and Banach spaces. It is determined for an extensive circle of readers, from students up to experts in science and also for specialists in the field.

### MSC:

 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 35Q30 Navier-Stokes equations 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 76D06 Statistical solutions of Navier-Stokes and related equations 76D07 Stokes and related (Oseen, etc.) flows 35Q35 PDEs in connection with fluid mechanics