On the blow-up criterion for solutions of 3D fractional Navier-Stokes equations
The existence of solutions to the fractional 3D incompressible Navier-Stokes equations in homogeneous Sobolev spaces (H˙) s is firstly proved in this paper,where α>1/2,max{5/2-2α,0}<s<3/2.Secondly,when the maximum time Tν∗ is finite,the blow-up in (H˙) s spaces and the decay in L2 norm of the solution and the lower bounds estimate of the solution with respect to L1 norm of Fourier transform are studied,via using the property of Fourier transform,interpolation results and product law in the homogeneous Sobolev spaces.Finally,it's a generalization of the results obtained by Benameur J,et al(2010)on the classical Navier-Stokes equations.
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