We prove unique existence of local-in-time smooth solutions of the Navier-Stokes equations for initial data in $L^{p}$ and $p \in [3, \infty)$ in an infinite cylinder, subject to the Neumann boundary condition.
Near identity transformations for the Navier-Stokes equations
Edge-degenerate families of $Ψ$Do's on an infinite cylinder
Quantitative lower bound for lifespan for solution of Navier-Stokes equations
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