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• W1593707948 abstract "These notes originate from a graduate course given at the University of Pisa during the spring semester 2007. They were completed while the author was visiting the Centro di Ricerca Matematica Ennio De Giorgi in february 2008. The main objective is to present at the level of beginners an introduction to several modern tools of micro-local analysis which are useful for the mathematical study of nonlinear partial differential equations. The guideline is to show how one can use the para-differential calculus to prove energy estimates using para-differential symmetrizers, or to decouple and reduce systems to equations. In these notes, we have concentrated the applications on the well posed-ness of the Cauchy problem for nonlinear PDE's. These notes are divided in three parts. Part I is an introduction to evolution equations. After the presentation of physical examples, we give the bases of the analysis of systems with constant coefficients. In Part II, we give an elementary and self-contained presentation of the para-differential calculus which was introduced by Jean-Michel Bony cite{Bony} in 1979. Part III is devoted to two applications. First we study quasi-linear hyperbolic systems. The second application concerns the local in time well posedness of the Cauchy problem for systems of Schodinger equations, coupled though quasilinear interactions." @default.
• W1593707948 created "2016-06-24" @default.
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• W1593707948 date "2008-08-27" @default.
• W1593707948 modified "2023-10-03" @default.
• W1593707948 title "Para-Differential Calculus and Applications to the Cauchy Problem for Nonlinear Systems" @default.
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