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

摘要

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 Gerard [American Journal of Mathematics 121 (1999), 131-175] and Merle and Vega [International Mathematics Research Notices 8 (1998), 399-425].