Profile decompositions for critical Lebesgue and Besov space embeddings

Details Profile decompositions for critical Lebesgue and Besov space embeddings Profile decompositions for critical Lebesgue and Besov space embeddings

2010-06-15

arxiv.org/abs/1006.3064v2

Mathematics

Analysis of PDEs

30 pages

Scientific paper

Profile decompositions for "critical" Sobolev-type embeddings are established, allowing one to regain some compactness despite the non-compact nature of the embeddings. Such decompositions have wide applications to the regularity theory of nonlinear partial differential equations, and have typically been established for spaces with Hilbert structure. Following the method of S. Jaffard, we treat settings of spaces with only Banach structure by use of wavelet bases. This has particular applications to the regularity theory of the Navier-Stokes equations, where many natural settings are non-Hilbertian.

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