Global well-posedness for fractional Navier-Stokes equations in variable exponent Fourier-Besov-Morrey spaces. (English) Zbl 1513.35419
Summary: 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.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35K55 | Nonlinear parabolic equations |
| 35R11 | Fractional partial differential equations |
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