Synopses & Reviews
This book is devoted to the evolution of infinite systems interacting via a short range potential. The Hamilton dynamics is defined through its evolution semigroup and the corresponding Bogolubov-Born-Green-Kirkwood-Yvo n (BBGKY) hierarchy is constructed. The existence of global in time solutions of the BBGKY hierarchy for hard spheres interacting via a short range potential is proved in the Boltzmann-Grad limit and by Bogolubov's and Cohen's methods. Audience: This volume will be of interest to graduate students and researchers whose work involves mathematical and theoretical physics, functional analysis and probability theory.
Synopsis
As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in- teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me- chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily provides the required justification. However things are not so easy, if we take a step forward and consider a gas is not in equilibrium, as is, e.g., the case for air around a flying vehicle. Questions of this kind have been asked since the dawn of the kinetic theory of gases, especially when certain results appeared to lead to paradoxical conclu- sions. Today this matter is rather well understood and a rigorous kinetic theory is emerging. The importance of these developments stems not only from the need of providing a careful foundation of such a basic physical theory, but also to exhibit a prototype of a mathematical construct central to the theory of non-equilibrium phenomena of macroscopic size.
Synopsis
This work is devoted to the evolution of infinite systems interacting via a short range potential. The Hamilton dynamics is defined through its evolution semigroup and the corresponding BBGKY hierarchy is constructed.
Description
Includes bibliographical references (p. [233]-242) and index.
Table of Contents
Introduction. I. The BBGKY Hierarchy. II. The Initial Value Problem for the BBGKY Hierarchy of a System of a Finite Number of Particles. III. The Initial Value Problem for LINFINITY Data: Thermodynamic Limit. IV. The Derivation of the Boltzmann Equation. V. On the Derivation of Kinetic Equations from the BBGKY Hierarchy. References. Subject Index.