GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

doi:10.1007/s10473-021-0109-1

Abstract

Abstract: In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space $\mathcal{F\dot{N}}_{p(\cdot),h(\cdot),q}^{s(\cdot)}(\mathbb{R}^3)$ with $s(\cdot) = 4-2\alpha-\frac{3}{p(\cdot)} $. We prove global well-posedness result with small initial data belonging to $\mathcal{F\dot{N}}_{p(\cdot),h(\cdot),q}^{4-2\alpha-\frac{3}{p(\cdot)} }(\mathbb{R}^3)$. The result of this paper extends some recent work.

Key words: fractional Navier-Stokes equations, global well-posedness, Fourier-Besov-Morrey space

CLC Number:

35Q30

Muhammad Zainul ABIDIN, Jiecheng CHEN. GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES[J].Acta mathematica scientia,Series B, 2021, 41(1): 164-176.

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References

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