Para-differential calculus and applications to the Cauchy problem for nonlinear systems. (English) Zbl 1156.35002

Métivier, Guy

Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series (Nuova Serie) 5. Pisa: Edizioni della Normale (ISBN 978-88-7642-329-1/pbk). xi, 140 p. (2008).

The main objective of this book is the para-differential technique, which was initiated by J. M. Bony. The para-differential calculus combines a linearization procedure for nonlinear equations, and a symbolic calculus which extends the classical Fourier analysis and pseudo-differential calculus. This book presented at the level of beginners an introduction to microlocal analysis and para-differential calculus. It also introduces the applications of these techniques to the Cauchy problem for nonlinear hyperbolic equations and Schrödinger equations. The book contains the author’s plentiful experience in this field.

Reviewer: Chen Shuxing (Shanghai)

MSC:

35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
35S50	Paradifferential operators as generalizations of partial differential operators in context of PDEs
35L15	Initial value problems for second-order hyperbolic equations
35Q55	NLS equations (nonlinear Schrödinger equations)
35A27	Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs

Keywords:

Schrödinger equations; nonlinear hyperbolic systems; linearization procedure; symbolic calculus