An introduction to Navier-Stokes equation and oceanography / Luc Tartar

The central theme of this book is functional analytic treatment of the Navier-Stokes equations with particular focusing on issues in connection with mathematical models used in Oceanography. The book is an adapted and slightly enlarged and revised version of lecture notes from a graduate course that the author held at Carnegie Mellon University in 1999, initially under the title “Partial Differential Equations Models in Oceanography". The author's mathematical approach to the subject reflects the spirit of the pioneering works of Jean Leray and Olga Ladyzhenskaya, the two famous mathematicians in this field who the author had known personally and to whom too he dedicates his book in their memory and in admiration of their achievements. The book consists of 44 lectures, completed with preface, introduction, detailed description of the lectures, bibliographical information, abbreviations and mathematical notation, references, and index. The author describes the general techniques for nonlinear partial differential equations that the he had developed, comprising, among others, the useful topics homogenization, compensated compactness and H-measures. Five lectures are explicitly devoted to or contain material connected with Sobolev spaces and the Sobolev embedding theorem. Explicitly stated theorems and lemmas are provided with proofs. (Zentralblatt)

Bibliogr. p. [241]-242. Notes bibliogr. Index