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Navier–Stokes equations with external forces in time‐weighted Besov spaces

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  • Hideo Kozono
  • Senjo Shimizu

Abstract

We show existence theorem of global mild solutions with small initial data and external forces in the time‐weighted Besov space which is an invariant space under the change of scaling. The result on local existence of solutions for large data is also discussed. Our method is based on the Lp‐Lq estimate of the Stokes equations in Besov spaces. Since we construct the global solution by means of the implicit function theorem, as a byproduct, its stability with respect to the given data is necessarily obtained.

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  • Hideo Kozono & Senjo Shimizu, 2018. "Navier–Stokes equations with external forces in time‐weighted Besov spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 291(11-12), pages 1781-1800, August.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:11-12:p:1781-1800
    DOI: 10.1002/mana.201700078
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    Cited by:

    1. Kazuhiro Ishige & Tohru Ozawa & Senjo Shimizu & Yasushi Taniuchi, 2022. "Preface," Partial Differential Equations and Applications, Springer, vol. 3(4), pages 1-9, August.

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