In this expository note, we collect some recent results concerning the applications of methods from dispersive and hyperbolic equations to the study of regularity criteria for the Navier-Stokes equations. In particular, these methods have recently been used to give an alternative approach to the Navier-Stokes regularity criterion of Escauriaza, Seregin and Šverák. The key tools are profile decompositions for bounded sequences of functions in critical spaces.
@article{JEDP_2010____A12_0,
author = {Koch, Gabriel S.},
title = {Profile decompositions and applications to {Navier-Stokes}},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {12},
pages = {1--13},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2010},
doi = {10.5802/jedp.69},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.69/}
}
TY - JOUR AU - Koch, Gabriel S. TI - Profile decompositions and applications to Navier-Stokes JO - Journées équations aux dérivées partielles PY - 2010 SP - 1 EP - 13 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.69/ DO - 10.5802/jedp.69 LA - en ID - JEDP_2010____A12_0 ER -
Koch, Gabriel S. Profile decompositions and applications to Navier-Stokes. Journées équations aux dérivées partielles (2010), article no. 12, 13 p. doi : 10.5802/jedp.69. http://www.numdam.org/articles/10.5802/jedp.69/
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