Abstract
This paper is concerned with the global well-posedness of the n-dimensional generalized incompressible Navier–Stokes equations with initial data in the critical Besov space. By fully using the advantage of suitable weighted functions and the Fourier localization technique, the global well-posedness is obtained without the hypothesis of smallness on initial data, but for some nonlinear smallness of the first iterate. We also give an example of initial data satisfying the nonlinear smallness condition, but whose norm is arbitrarily large.
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The author would glad to acknowledge his sincere thanks to the Professor Song Jiang for many valuable comments and suggestions.
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Communicated by Yong Zhou.
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This work is partially supported by the National Natural Science Foundation of China (11401202), the Scientific Research Fund of Hunan Provincial Education Department (14B117), and the China Postdoctoral Science Foundation (2015M570053).
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Liu, Q. Global Well-Posedness of the Generalized Incompressible Navier–Stokes Equations with Large Initial Data. Bull. Malays. Math. Sci. Soc. 43, 2549–2564 (2020). https://doi.org/10.1007/s40840-019-00818-5
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DOI: https://doi.org/10.1007/s40840-019-00818-5