Global well-posedness for Navier–Stokes equations in critical Fourier–Herz spaces

We prove the global well-posedness for the 3D Navier–Stokes equations in critical Fourier–Herz spaces, by making use of the Fourier localization method and the Littlewood–Paley theory. The advantage of working in Fourier–Herz spaces lies in that they are more adapted than classical Besov spaces, for...

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Veröffentlicht in:Nonlinear analysis Jg. 75; H. 9; S. 3754 - 3760
Hauptverfasser: Cannone, Marco, Wu, Gang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.06.2012
Elsevier
Schlagworte:
Fourier analysis
Fourier–Herz spaces
Global well-posedness
Localization method
Mathematical analysis
Mathematical Physics
Mathematics
Navier-Stokes equations
Nonlinearity
Regularity
Theorems
Three dimensional
Navier–Stokes equations
Global well-posedness
Fourier–Herz spaces
ISSN:0362-546X, 1873-5215
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Zusammenfassung:We prove the global well-posedness for the 3D Navier–Stokes equations in critical Fourier–Herz spaces, by making use of the Fourier localization method and the Littlewood–Paley theory. The advantage of working in Fourier–Herz spaces lies in that they are more adapted than classical Besov spaces, for estimating the bilinear paraproduct of two distributions with the summation of their regularity indexes exactly zero. Our result is an improvement of a recent theorem by Lei and Lin (2011) [10].
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2012.01.029