The Navier-Stokes equations with the Neumann boundary condition in an infinite cylinder (Q2326787)

In this paper, the author is concerned with the 3D Navier-Stokes-equations subject to the Neumann boundary condition for the infinite cylinder. An initial condition is supplemented, too. The author is going to prove the unique existence of loc-in-time smooth solutions to the problem described before for initial data in \(L^p\) and \(p \in [3, \infty)\). Different functional-analytic tools are used in order to prove the main theorem. Thus, the author applied Young's inequality, various a priori estimates, fractional powers of differential operators. and much more. The paper is comparable comprehensive. It contains 39 items.