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On a new scale of regularity spaces with applications to Euler’s equations. (English) Zbl 0983.35100
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.

MSC:
35Q05 Euler-Poisson-Darboux equations
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
42B35 Function spaces arising in harmonic analysis
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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