Reduction and a concentration-compactness principle for energy-Casimir functionals (Q2782960)

The paper is concerned with the existence of minimizers for energy-Casimir functionals \({\mathcal{H}}_{{\mathcal{C}}}\). The author constructs reduced functionals \({\mathcal{H}}^r_{{\mathcal{C}}}\) which act on the space of spatial mass densities and shows how a minimizer of \({\mathcal{H}}^r_{{\mathcal{C}}}\) induces a minimizer of \({\mathcal{H}}_{{\mathcal{C}}}\). He also proves a concentration compactness principle which yields a minimizer of \({\mathcal{H}}^r_{{\mathcal{C}}}\). This generalizes the techniques from earlier work of \textit{Y. Guo} and the author [Commun. Math. Phys. 219, 607-629 (2001; Zbl 0974.35093)].