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Author : Dongxiao Yu
Release : 2024-07-25
Genre : Mathematics
Kind : eBook
Book Rating : 489/5 ( reviews)
Book Synopsis Asymptotic Completeness for a Scalar Quasilinear Wave Equation Satisfying the Weak Null Condition by : Dongxiao Yu
Download or read book Asymptotic Completeness for a Scalar Quasilinear Wave Equation Satisfying the Weak Null Condition written by Dongxiao Yu. This book was released on 2024-07-25. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Author :
Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Mathematical Reviews by :
Download or read book Mathematical Reviews written by . This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Demetrios Christodoulou
Release : 2014-07-14
Genre : Mathematics
Kind : eBook
Book Rating : 171/5 ( reviews)
Book Synopsis The Global Nonlinear Stability of the Minkowski Space (PMS-41) by : Demetrios Christodoulou
Download or read book The Global Nonlinear Stability of the Minkowski Space (PMS-41) written by Demetrios Christodoulou. This book was released on 2014-07-14. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Alexandru D. Ionescu
Release : 2022-03-15
Genre : Science
Kind : eBook
Book Rating : 039/5 ( reviews)
Book Synopsis The Einstein-Klein-Gordon Coupled System by : Alexandru D. Ionescu
Download or read book The Einstein-Klein-Gordon Coupled System written by Alexandru D. Ionescu. This book was released on 2022-03-15. Available in PDF, EPUB and Kindle. Book excerpt: A definitive proof of global nonlinear stability of Minkowski space-time as a solution of the Einstein-Klein-Gordon equations This book provides a definitive proof of global nonlinear stability of Minkowski space-time as a solution of the Einstein-Klein-Gordon equations of general relativity. Along the way, a novel robust analytical framework is developed, which extends to more general matter models. Alexandru Ionescu and Benoît Pausader prove global regularity at an appropriate level of generality of the initial data, and then prove several important asymptotic properties of the resulting space-time, such as future geodesic completeness, peeling estimates of the Riemann curvature tensor, conservation laws for the ADM tensor, and Bondi energy identities and inequalities. The book is self-contained, providing complete proofs and precise statements, which develop a refined theory for solutions of quasilinear Klein-Gordon and wave equations, including novel linear and bilinear estimates. Only mild decay assumptions are made on the scalar field and the initial metric is allowed to have nonisotropic decay consistent with the positive mass theorem. The framework incorporates analysis both in physical and Fourier space, and is compatible with previous results on other physical models such as water waves and plasma physics.
Author : Yvonne Choquet-Bruhat
Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 722/5 ( reviews)
Book Synopsis General Relativity and the Einstein Equations by : Yvonne Choquet-Bruhat
Download or read book General Relativity and the Einstein Equations written by Yvonne Choquet-Bruhat. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.
