Global existence results for the Navier–Stokes equations in the rotational framework in Fourier–Besov spaces

Daoyuan Fang, Bin Han, Matthias Georg Hieber

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

Consider the equations of Navier–Stokes in ℝ3 in the rotational setting, i.e., with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided the initial data is small with respect to the norm of the Fourier–Besov space ḞB2−3/p p,r (ℝ3), where p ∈ (1,∞] and r ∈ [1,∞]. In the two-dimensional setting, a unique, global mild solution to this set of equations exists for non-small initial data u0 ∈ Lp σ(ℝ2) for p ∈ [2,∞).

Original languageEnglish
Title of host publicationOperator Theory: Advances and Applications
PublisherSpringer International Publishing
Pages199-211
Number of pages13
Volume250
Publication statusPublished - 2015
Externally publishedYes

Publication series

NameOperator Theory: Advances and Applications
Volume250
ISSN (Print)02550156
ISSN (Electronic)22964878

Fingerprint

Global Existence
Existence Results
Navier-Stokes Equations
Mild Solution
Coriolis Force
P-space
Navier-Stokes
Norm
Framework

Keywords

  • Global existence
  • Navier–Stokes
  • Rotational framework

ASJC Scopus subject areas

  • Analysis

Cite this

Fang, D., Han, B., & Hieber, M. G. (2015). Global existence results for the Navier–Stokes equations in the rotational framework in Fourier–Besov spaces. In Operator Theory: Advances and Applications (Vol. 250, pp. 199-211). (Operator Theory: Advances and Applications; Vol. 250). Springer International Publishing.

Global existence results for the Navier–Stokes equations in the rotational framework in Fourier–Besov spaces. / Fang, Daoyuan; Han, Bin; Hieber, Matthias Georg.

Operator Theory: Advances and Applications. Vol. 250 Springer International Publishing, 2015. p. 199-211 (Operator Theory: Advances and Applications; Vol. 250).

Research output: Chapter in Book/Report/Conference proceedingChapter

Fang, D, Han, B & Hieber, MG 2015, Global existence results for the Navier–Stokes equations in the rotational framework in Fourier–Besov spaces. in Operator Theory: Advances and Applications. vol. 250, Operator Theory: Advances and Applications, vol. 250, Springer International Publishing, pp. 199-211.
Fang D, Han B, Hieber MG. Global existence results for the Navier–Stokes equations in the rotational framework in Fourier–Besov spaces. In Operator Theory: Advances and Applications. Vol. 250. Springer International Publishing. 2015. p. 199-211. (Operator Theory: Advances and Applications).
Fang, Daoyuan ; Han, Bin ; Hieber, Matthias Georg. / Global existence results for the Navier–Stokes equations in the rotational framework in Fourier–Besov spaces. Operator Theory: Advances and Applications. Vol. 250 Springer International Publishing, 2015. pp. 199-211 (Operator Theory: Advances and Applications).
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