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Following Gr\\\"{u}nrock's result in 3D, we take the data in the Fourier-Lebesgue spaces $\\^{H}_s^r$, which coincide with the Sobolev spaces of the same regularity for $r=2$, but scale like lower regularity Sobolev spaces for $1<r<2$. We show local well-posedness (LWP) for the range of exponents $s>1+\\frac{3}{2r}$, $1<r\\leq 2$. 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