Zakharov system in two space dimensions. (January 2022)

• Record Type: Journal Article
• Authors: Ozawa, Tohru; Tomioka, Kenta
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: 35Q55 -- 35A35 -- 35B30 -- 35L70 -- 82D10; Zakharov system -- Global solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112532
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the Cauchy problem for the Zakharov system in a two dimensional domain. Under natural assumptions on the data, we prove the existence and uniqueness of global solutions in H 2 ⊕ H 1 . The method of the construction of global solutions depends on the proof that solutions of some regularized system form a bounded sequence in H 2 ⊕ H 1 and a Cauchy sequence in H 1 ⊕ L 2 . The method of proof is independent of the compactness argument and Brezis–Gallouet inequality.