FrontiersThe Cauchy problem for fractional Navier-Stokes equations in Sobolev spaces

In this paper we use the tools from harmonic analysis to study the Cauchy problem for Navier-Stokes equations with time-fractional derivative of order α ∈ (0, 1), which can be used to simulate the anomalous diffusion in fractal media. Two main results concerning the local existence of solutions for the given problem in Sobolev space are addressed.