High frequency approximation of solutions to Klein–Gordon equation in Orlicz framework

Article type: Research Article

Authors: Ben Ayed, Ines

Affiliations: Faculté des Sciences de Tunis, LR03ES04 Équations aux dérivées partielles et applications, Université de Tunis El Manar, 2092 Tunis, Tunisie. E-mail: [email protected]

Abstract: In this paper, we investigate the behavior of solutions to 2D Klein–Gordon equation in the framework of Orlicz norm. The analysis we conducted in this article, which is based on profiles decompositions, emphasizes the distinguished role played by the 1-oscillating component of the sequence of the Cauchy data. This phenomenon is strikingly different from those obtained in previous works, such as in Bahouri and Gérard [American Journal of Mathematics 121 (1999), 131–175] and Merle and Vega [International Mathematics Research Notices 8 (1998), 399–425].

Keywords: Free Klein–Gordon equation, Olicz space, profile decomposition

DOI: 10.3233/ASY-161398

Journal: Asymptotic Analysis, vol. 101, no. 3, pp. 181-206, 2017