An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Volume 1: Linearized Steady Problems: Linearized Steady Problems v. 1 (Applied Mathematical Sciences) Book

This work is a systematic and up-to-date investigation of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions in bounded as well as unbounded domains. When the region of flow is unbounded, asymptotic behavior is also investigated. The problems are treated within the framework of Lebesgue spaces, such a general approach allowing for a comprehensive and unified treatment.

The subject is divided into two volumes, which deal with steady flow (boundary value problem). Each volume is self-contained. In both volumes, the nonlinear analysis is preceded and supported by a suitable linear analysis; however, the nonlinear analysis is treated to a large extent due to independent interest.

This volume examines linearised approximations of the steady-state Navier-Stokes problem – specifically, the Stokes problem in bounded and exterior domains as well as in domains with noncompact boundaries. Moreover, Oseen equations and the associated boundary value problem are investigated in exterior domains.

This new edition has been revised and updated throughout to take into account the recent significant contributions to the field. A new chapter is dedicated to the motion of a rigid body in a fluid in the Stokes regime, which has found increased interest due to questions related to liquid-particle interactions.

The books are addressed to students (both graduate and advanced undergraduate) and to all mathematicians and applied mathematicians who wish to become acquainted with the subject.