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

Abstract

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

arXiv admin note: text overlap with arXiv:1003.2562, arXiv:1112.2998 by other authors

References in corpus (1)

• An inverse theorem for the bilinear $L^2$ Strichartz estimate for the wave equation