Tartar An Introduction to Navier-Stokes Equation and Oceanography

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

E-Book, Englisch, Band 1, 247 Seiten

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.

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.

Autoren/Hrsg.

Tartar, Luc

Inhaltsverzeichnis

1;Preface;7
2;Introduction;15
3;Detailed Description of Lectures;18
4;Contents;25
5;Basic physical laws and units;28
6;Radiation balance of atmosphere;33
7;Conservations in ocean and atmosphere;37
8;Sobolev spaces I;41
9;Particles and continuum mechanics;49
10;Conservation of mass and momentum;57
11;Conservation of energy;63
12;One-dimensional wave equation;68
13;Nonlinear e.ects, shocks;74
14;Sobolev spaces II;82
15;Linearized elasticity;88
16;Ellipticity conditions;93
17;Sobolev spaces III;97
18;Sobolev spaces IV;101
19;Sobolev spaces V;106
20;Sobolev embedding theorem;110
21;Fixed point theorems;117
22;Brouwer’s topological degree;123
23;Time-dependent solutions I;128
24;Time-dependent solutions II;134
25;Time-dependent solutions III;139
26;Uniqueness in 2 dimensions;145
27;Traces;148
28;Using compactness;155
29;Existence of smooth solutions;160
30;Semilinear models;164
31;Size of singular sets;172
32;Local estimates, compensated integrability;177
33;Coriolis force;182
34;Equation for the vorticity;185
35;Boundary conditions in linearized elasticity;187
36;Turbulence, homogenization;191
37;G-convergence and H-convergence;195
38;One-dimensional homogenization, Young;200
39;measures;200
40;Nonlocal e.ects I;204
41;Nonlocal e.ects II;209
42;A model problem;213
43;Compensated compactness I;217
44;Compensated compactness II;221
45;Di.erential forms;224
46;The compensated compactness method;229
47;H-measures and variants;235
48;Biographical Information;243
49;Abbreviations and Mathematical Notation;247
50;References;251
51;Index;253