On global solutions of a Zakharov type system. (24th August 2015)

• Record Type: Journal Article
• Authors: Beck, Thomas; Pusateri, Fabio; Sosoe, Phil; Wong, Percy
• Is Part Of: Nonlinearity. Volume 28:Number 9(2015:Sep.)
• Page Start: 3419
• Page End: 3441
• Publication Date: 2015-08-24
• Subjects: Zakharov system -- global solutions -- Yukawa system; 35L52 -- 35L71; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/9/3419
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider a class of wave-Schrödinger systems in three dimensions with a Zakharov-type coupling. This class of systems is indexed by a parameter γ which measures the strength of the null form in the nonlinearity of the wave equation. The case corresponds to the well-known Zakharov system, while the case corresponds to the Yukawa system. Here we show that sufficiently smooth and localized Cauchy data lead to pointwise decaying global solutions which scatter, for any .