BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS

Sergiù Klainerman, Sigmund Selberg

Type: Article

Publication Date: 2002-05-01

Citations: 155

DOI: https://doi.org/10.1142/s0219199702000634

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.

Locations

arXiv (Cornell University) - View - PDF
Communications in Contemporary Mathematics - View

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+	On the Regularity Properties of the Wave Equation	1994	Sergiù Klainerman Matei Machedon
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+ PDF Chat	Oscillatory integrals and multiplier problem for the disc	1972	Lennart Carleson Per Sjölin
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+	The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices	1993	Carlos E. Kenig Gustavo Ponce Luis Vega
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