Tartar An Introduction to Navier-Stokes Equation and Oceanography

2006
ISBN: 978-3-540-36545-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1, 247 Seiten, eBook

Reihe: Lecture Notes of the Unione Matematica Italiana

This text corresponds to a graduate mathematics course taught at Carnegie Mellon University in the spring of 1999. Included are comments added to the lecture notes, a bibliography containing 23 items, and brief biographical information for all scientists mentioned in the text, thus showing that the creation of scientific knowledge is an international enterprise.

Zielgruppe

Research

Autoren/Hrsg.

Tartar, Luc

Inhaltsverzeichnis

Introduction.- Basic physical laws and units.- Radiation balance of atmosphere.- Conservations in ocean and atmosphere.- Sobolev spaces I.- Particles and continuum mechanics.- Conservation of mass and momentum.- Conservation of energy.- One-dimensional wave equation.- Nonlinear effects, shocks.- Sobolev spaces II.- Linearized elasticity.- Ellipticity conditions.- Sobolev spaces III.- Sobolev spaces IV.- Sobolev spaces V.- Sobolev embedding theorem.- Fixed point theorems.- Brouwer's topological degree.- Time-dependent solutions I.- Time-dependent solutions II.- Time-dependent solutions III.- Uniqueness in 2 dimensions.- Traces.- Using compactness.- Existence of smooth solutions.- Semilinear models.- Size of singular sets.- Local estimates, compensated integrability.- Coriolis force.- Equation for the vorticity.- Boundary conditions in linearized elasticity.- Turbulence, homogenization.- G-convergence and H-convergence.- One-dimensional homogenization, Young measures.- Nonlocal effects I.- Nonlocal effects II.- A model problem.- Compensated compactness I.- Compensated compactness II.- Differential forms.- The compensated compactness method.- H-measures and variants.- Biographical Information.- Abbreviations and Mathematical Notation.- References.- Index.

Über Autor(innen)

Luc Tartar studied at Ecole Polytechnique in Paris, France, 1965-1967, where he was taught by Laurent Schwartz and Jacques-Louis Lions in mathematics, and by Jean Mandel in continuum mechanics.

He did research at Centre National de la Recherche Scientifique, Paris, France, 1968-1971, working under the direction of Jacques-Louis Lions for his thèse d'état, 1971.

He taught at Université Paris IX-Dauphine, Paris, France, 1971-1974, at University of Wisconsin, Madison, WI, 1974-1975, at Université de Paris-Sud, Orsay, France, 1975-1982.

He did research at Commissariat à l'Energie Atomique, Limeil, France, 1982-1987.

In 1987, he was elected Correspondant de l'Académie des Sciences, Paris, in the section Mécanique.

Since 1987 he has been teaching at Carnegie Mellon University, Pittsburgh, PA, where he has been University Professor of Mathematics since 1994.

Partly in collaboration with François Murat, he has specialized in the development of new mathematical tools for solving the partial differential equations of continuum mechanics (homogenization, compensated compactness, H-measures), pioneering the study of microstructures compatible with the partial differential equations describing the physical balance laws, and the constitutive relations.

He likes to point out the defects of many of the models which are used, as a natural way to achieve the goal of improving our understanding of mathematics and of continuum mechanics.