期刊
INDIANA UNIVERSITY MATHEMATICS JOURNAL
卷 59, 期 5, 页码 1801-1830出版社
INDIANA UNIV MATH JOURNAL
DOI: 10.1512/iumj.2010.59.4426
关键词
Profile decomposition; concentration compactness; Sobolev embedding; wavelets; nonlinear approximation; Navier-Stokes equation
类别
资金
- EPSRC [EP/E035027/1]
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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