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Mathematics > Analysis of PDEs

arXiv:1006.3064 (math)
[Submitted on 15 Jun 2010 (v1), last revised 17 Jun 2010 (this version, v2)]

Title:Profile decompositions for critical Lebesgue and Besov space embeddings

Authors:Gabriel S. Koch
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Abstract: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.
Comments: 30 pages
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1006.3064 [math.AP]
  (or arXiv:1006.3064v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1006.3064
Journal reference: Indiana Univ. Math. J. 59 No. 5 (2010), 1801-1830
Related DOI: https://doi.org/10.1512/iumj.2010.59.4426

Submission history

From: Gabriel Koch [view email]
[v1] Tue, 15 Jun 2010 19:50:17 UTC (22 KB)
[v2] Thu, 17 Jun 2010 10:15:11 UTC (22 KB)
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