Abstract
We consider instationary Navier–Stokes equations with prescribed time-dependent fluxes in a cylindrical domain \(\Omega \subset {\mathbb R}^n,n\ge 3,\) with several exits to infinity. First, we prove existence and uniqueness of time-dependent Poiseuille flow in \(L^q\)-spaces on infinite straight cylinders over time interval \((0,T)\), \(0 2, q\in (\frac{n-1}{2},\infty )\), with an exponential weight along the axial directions of \(\Omega \).
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