The Navier–Stokes equations with the Neumann boundary condition in an infinite cylinder

• Published in: Manuscripta mathematica Vol. 160; no. 3-4; pp. 359 - 383
• Main Author: Abe, K.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2019; Springer Nature B.V
• Subjects: Algebraic Geometry; Boundary conditions; Calculus of Variations and Optimal Control; Optimization; Cylinders; Fluid dynamics; Fluid flow; Geometry; Lie Groups; Mathematical analysis; Mathematics; Mathematics and Statistics; Navier-Stokes equations; Number Theory; Topological Groups; 35Q35; 35K90

We prove unique existence of local-in-time smooth solutions of the Navier–Stokes equations for initial data in L p and p ∈ [ 3 , ∞ ) in an infinite cylinder, subject to the Neumann boundary condition.