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Uniqueness of mild solutions of the Navier-Stokes equation and maximal Lp-regularity

✍ Scribed by Sylvie Monniaux

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 346 KB
Volume: 328
Category: Article
ISSN: 0764-4442
DOI: 10.1016/s0764-4442(99)80231-6

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✦ Synopsis

In this Note, we give a new proof of the uniqueness of mild solutions of the Navier-Stokes equation in C([O!T); (L,'(R"))'). Th e main tool of the proof is the maximal L"-regularity of the Laplacian in (L" (W"))". 0 AcadCmie des Sciences/Elsevier, Paris Unicit6 des solutions CC mild )j de I'Gquation de Nuvier-Stokes et ri$plaritt? maximale L" R&urn& Duns cette Note. on donne une nouvelle preuve de l'unicite' des solutions N mild JJ de I'e'quution de Nuvier-Stokes duns C( [O. T) : (L" (W"))"). Celle-ci repose essentiellernent sur lu re'gulnrite' mnximale I. P du laplacien duns (ti'(W" ))". 0 AcadCmie des Sciences/Elsevier. Paris

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