An introduction to the mathematical theory of the Navier-Stokes equations

Abstract

The motivation for this addition comes from the increasing effort that mathematicians, especially over the past decade, have devoted to problems describing the interaction of a viscous liquid with rigid bodies. For this reason, I dedicated the above chapters to a systematic and updated analysis of a fundamental question of liquid–solid interaction, namely, the steady flow of a viscous liquid around a body that is allowed to translate and to rotate. In the years 2003 through 2010, over fifty relevant mathematical papers, directly or indirectly dedicated to this subject, have been published. Therefore, I deem it very useful for the interested researcher to have a place where all significant basic results are collected and treated in an organized and detailed fashion. Furthermore, several important new contributions to the field that were published after 1998 have led me to update numerous sections extensively, as well as to add other new ones, not to mention the corresponding substantial increase in the number of bibliographic items. Among the above contribu- tions, I would like to point out especially those dedicated to the regularity of solutions to the nonlinear problem in arbitrary dimension, as well as those concerning the asymptotic behavior in two-dimensional exterior domains.