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

International audienceThis paper is devoted to the description of the lack of compactness of the Sobolev space H 2 rad (R 4) in the Orlicz space 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 L(R 2) in [H. Bahouri, M. Majdoub and N. Masmoudi, On the lack of compactness in the 2D critical Sobolev embedding, J. Funct. Anal. 260 (2011) 208–252]