Characterization of the lack of compactness of $H^2_{rad}(\R^4)$ into the Orlicz space

Abstract

This paper is devoted to the description of the lack of compactness of the Sobolev space $H^2_{rad}(\R^4)$ in the Orlicz space $\mathcal{L}(\R^4)$. The approach that we adopt to establish this characterization is in the spirit of the one adopted in the case of $H^1_{rad}(\R^2)$ into the Orlicz space $\mathcal{L}(\R^2)$ in \cite{Bahouri}.