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A Remark on L ∞ Solutions to the 2-D Navier–Stokes Equations

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Abstract.

A single-exponential growth estimate of the solutions to the 2-dimensional Navier–Stokes equations in the whole space for nondecaying initial velocity is established. The crucial idea is to decompose velocity into high and low frequency parts. Moreover, if the linear term and the vorticity decay exponentially, the velocity is bounded uniformly in time.

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Authors and Affiliations

  1. Department of Mathematical Science, Waseda University, Shinjuku, 169-8555, Japan

    Okihiro Sawada

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

    Yasushi Taniuchi

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  1. Okihiro Sawada
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  2. Yasushi Taniuchi
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Correspondence to Okihiro Sawada.

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Communicated by Y. Giga

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Sawada, O., Taniuchi, Y. A Remark on L ∞ Solutions to the 2-D Navier–Stokes Equations. J. math. fluid mech. 9, 533–542 (2007). https://doi.org/10.1007/s00021-005-0212-4

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  • DOI: https://doi.org/10.1007/s00021-005-0212-4

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