Abstract
In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space \({\cal F}\dot {\cal N}_{p\left( \cdot \right),h\left( \cdot \right),q}^{s\left( \cdot \right)}\left( {{\mathbb{R}^3}} \right)\) with \(s\left( \cdot \right) = 4 - 2\alpha - {3 \over {p\left( \cdot \right)}}\). We prove global well-posedness result with small initial data belonging to \({\cal F}\dot {\cal N}_{p\left( \cdot \right),h\left( \cdot \right),q}^{4 - 2\alpha - {3 \over {p\left( \cdot \right)}}}\left( {{\mathbb{R}^3}} \right)\) The result of this paper extends some recent work.
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Acknowledgements
The authors would like to thank Dr. Ru Shaolei for useful discussions and helpful suggestions on this article.
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The research was supported by NSFC (11671363, 11701519).
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Abidin, M.Z., Chen, J. Global well-posedness for fractional Navier-Stokes equations in variable exponent Fourier-Besov-Morrey spaces. Acta Math Sci 41, 164–176 (2021). https://doi.org/10.1007/s10473-021-0109-1
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DOI: https://doi.org/10.1007/s10473-021-0109-1