Borel summability of Navier-Stokes equation in ${\mathbb{R}}^3$ and small time existence

O. Costin, S. Tanveer

We consider the Navier-Stokes initial value problem, $$v_t - \nabla v = -\mathcal{P} [ v \cdot \nabla v \right ] + f, v(x, 0) = v_0 (x), x \in \mathbb{R}^3 $$ where $\mathcal{P}$ i…