Equations de Navier-Stokes dans ℝ2: Existence et comportement asymptotique de solutions d'énergie infinie

Pierre Germain

doi:10.1016/j.bulsci.2005.06.004

Equations de Navier-Stokes dans ℝ²: Existence et comportement asymptotique de solutions d'énergie infinie

Pierre Germain

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove first in this article that the two-dimensional Navier-Stokes equations are globally well-posed if the initial data u₀ belongs to the closure of the Schwartz class in ∂BMO. We show then the asymptotic convergence to zero of the solution u of (NS) for an initial data u₀ in some Besov space. Ḃ_p,q ^-1+2/p.

Original language	French
Pages (from-to)	123-151
Number of pages	29
Journal	Bulletin des Sciences Mathematiques
Volume	130
Issue number	2
DOIs	https://doi.org/10.1016/j.bulsci.2005.06.004
State	Published - Mar 2006

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1016/j.bulsci.2005.06.004

Cite this

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title = "Equations de Navier-Stokes dans ℝ2: Existence et comportement asymptotique de solutions d'{\'e}nergie infinie",

abstract = "We prove first in this article that the two-dimensional Navier-Stokes equations are globally well-posed if the initial data u0 belongs to the closure of the Schwartz class in ∂BMO. We show then the asymptotic convergence to zero of the solution u of (NS) for an initial data u0 in some Besov space. Ḃp,q -1+2/p.",

author = "Pierre Germain",

year = "2006",

month = mar,

doi = "10.1016/j.bulsci.2005.06.004",

language = "French",

volume = "130",

pages = "123--151",

journal = "Bulletin des Sciences Mathematiques",

issn = "0007-4497",

publisher = "Elsevier Masson s.r.l.",

number = "2",

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AB - We prove first in this article that the two-dimensional Navier-Stokes equations are globally well-posed if the initial data u0 belongs to the closure of the Schwartz class in ∂BMO. We show then the asymptotic convergence to zero of the solution u of (NS) for an initial data u0 in some Besov space. Ḃp,q -1+2/p.

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