DESCRIPTION OF THE LACK OF COMPACTNESS IN ORLICZ SPACES AND APPLICATIONS

Abstract

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