BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS-Reference-Cited by-同舟云学术

BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS

Published:2002-05 Issue:02 Volume:04 Page:223-295
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

KLAINERMAN SERGIU¹,SELBERG SIGMUND²

Affiliation:

1. Department of Mathematics, Princeton University, Princeton, New Jersey 08544, USA

2. Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218, USA

Abstract

We undertake a systematic review of results proved in [26, 27, 30-32] concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assumptions on the initial data. Moreover we give a considerably simplified and unified treatment of these results and provide also complete proofs for large data. The paper is also intended as an introduction to and survey of current research in the very active area of nonlinear wave equations. The key ingredients throughout the survey are the use of the null structure of the equations we consider and, intimately tied to it, bilinear estimates.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199702000634

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