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Existence of solutions on the whole time axis to the Navier-Stokes equations with precompact range in L 3

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We present an existence theorem of mild solutions on the whole time axis to the Navier-Stokes equations in unbounded domains \({\Omega\subset \mathbb{R}^3}\) having precompact range in \({L^3(\Omega)}\) if the external force is small and has precompact range in some function space. In our forthcoming paper [7] we proved the uniqueness of such solutions.

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Authors and Affiliations

  1. International Research Training Group Darmstadt-Tokyo (IRTG 1529), Technische Universität Darmstadt, 64289, Darmstadt, Germany

    Reinhard Farwig

  2. Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan

    Tomoyuki Nakatsuka

  3. Department of Mathematical Sciences, Shinshu University, Matsumoto, 390-8621, Japan

    Yasushi Taniuchi

Authors
  1. Reinhard Farwig
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  2. Tomoyuki Nakatsuka
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  3. Yasushi Taniuchi
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Correspondence to Tomoyuki Nakatsuka.

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Farwig, R., Nakatsuka, T. & Taniuchi, Y. Existence of solutions on the whole time axis to the Navier-Stokes equations with precompact range in L 3 . Arch. Math. 104, 539–550 (2015). https://doi.org/10.1007/s00013-015-0772-3

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  • DOI: https://doi.org/10.1007/s00013-015-0772-3

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