## Differential and Integral Equations

### Description of the lack of compactness in Orlicz spaces and applications

#### Abstract

In this paper, we investigate the lack of compactness of the Sobolev embedding of $H^1(\mathbb R^2)$ into the Orlicz space $L^{{\phi}_p}(\mathbb R^2)$ associated to the function $\phi_p$ defined by $\phi_p(s):={\rm{e}^{s^2}}-\sum_{k=0}^{p-1} \frac{s^{2k}}{k!}$. We also undertake the study of a nonlinear wave equation with exponential growth where the Orlicz norm $\|.\|_{L^{\phi_p}}$ plays a crucial role. This study includes issues of global existence, scattering and qualitative study.

#### Article information

Source
Differential Integral Equations, Volume 28, Number 5/6 (2015), 553-580.

Dates
First available in Project Euclid: 30 March 2015