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On stability of weak Navier–Stokes solutions with large L 3,∞ initial data

Abstract:

We consider the Cauchy problem for the Navier–Stokes equation in ℝ3×]0,∞[ with the initial datum (Formula presented.), a critical space containing nontrivial (−1)−homogeneous fields. For small (Formula presented.) one can get global well-posedness by perturbation theory. When (Formula presented.) is not small, the perturbation theory no longer applies and, very likely, the local-in-time well-posedness and uniqueness fails. One can still develop a good theory of weak solutions with the followi...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1080/03605302.2018.1449219

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Hildas College
Šverák, V More by this author
Publisher:
Taylor and Francis Publisher's website
Publication date:
2018-05-07
Acceptance date:
2017-10-21
DOI:
EISSN:
1532-4133
ISSN:
0360-5302
Pubs id:
pubs:853764
URN:
uri:5499bc63-6a40-4848-9950-f13a277e6052
UUID:
uuid:5499bc63-6a40-4848-9950-f13a277e6052
Local pid:
pubs:853764

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