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Global Large Solutions to the 3-D Generalized Incompressible Navier–Stokes Equations

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Abstract

In this paper, we prove the global well-posedness of the 3-D generalized incompressible Navier–Stokes equations in critical Besov spaces under a polynomial smallness assumption on the initial data. Moreover, we construct a class of initial data with large vertical component, which satisfies that polynomial condition but cannot satisfy the exponential condition in Liu (2020).

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Shunhang Zhang

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  1. Shunhang Zhang
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Correspondence to Shunhang Zhang.

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Communicated by Yong Zhou.

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Zhang, S. Global Large Solutions to the 3-D Generalized Incompressible Navier–Stokes Equations. Bull. Malays. Math. Sci. Soc. 44, 2101–2121 (2021). https://doi.org/10.1007/s40840-020-01051-1

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  • DOI: https://doi.org/10.1007/s40840-020-01051-1

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