On a new scale of regularity spaces with applications to Euler's equations (Q2722668)

The author introduces a new scale of spaces which fills the gap between \(L^{p,\infty}\) and the Morrey space \(M^p\), denoted by \(V^{p,q}\). A further logarithmic refinement parameter \(\alpha\) allows to introduce the space \(V^{p,q}(\log V)^{\alpha}\), and compact embeddings in appropriate Sobolev spaces are studied. The strong convergence of approximate Euler solutions is investigated showing that the new scale of spaces enables to approach the borderline between \(H^{-1}\)-compactness and the phenomena of concentration-cancellation.