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In this paper we show that the Euler equation for incompressible fluids in R2 is well posed in the (vector-valued) Lebesgue spaces
Ls
p = (1 - ∆)-s/2 Lp(R2) with s > 1 + 2/p, 1 < p < ∞
and that the same is true of the Navier-Stokes equation uniformly in the viscosity ν.
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