The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics.
The book focuses on incompressible deterministic Navier–Stokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.
“This book surely satisfies the requirements of those interested in this field of Physics. On the whole I think that this book can give, especially to a young reader, a certain feeling about the enthusiam and novelty of condensed matter research during the last three decades.”Il Nuovo Saggiatore, 2002
Reviews of the First Edition:
“This book collects a series of articles in which problems which had always been thought quite intractable are shown to be solved by simple, but clear thinking. Although the phrase “simple views” is justified by the clarity of de Gennes exposition, the problems had been unresolved for decades and it is a tribute to de Gennes' intuitive skill that he has been able to solve so many problems which are not only deep basic science, but also central in modern technology.”Sam Edwards
“For amateurs and connoisseurs — interested in physics, chemistry or biology — Pierre-Gilles de Gennes has opened his gentry-style 'cabinet de curiosités'. Miscellaneous products of his inventive industry, including the famous and the unfamous, are brought together in this self-selected collection, accompanied with recent hindsightful remarks of the Nobel laureate.”Gérard Toulouse
“This volume of collected works of Pierre-Gilles de Gennes will be a valuable and stimulating source for many years to come for younger readers and for beginners in the subfields of condensed matter covered in this volume, as well as a useful and compact reference book for all workers in the field.”Helmut R Brand