Global estimates in weighted spaces of weak solutions of the Navier-Stokes equations in exterior domains (Q1924984)

Consider the instationary Navier-Stokes equations in an exterior domain of \(\mathbb{R}^3\). Given arbitrarily large external data we construct a global suitable weak solution and, using weight functions \(|x|^\alpha\), \(\alpha\geq 0\), prove weighted integral estimates in space and time. Major tools are weighted estimates for the nonstationary Stokes system based on analytic semigroup theory in \(L^p\)-function spaces with Muckenhoupt weights and weighted energy estimates of a suitable weak solution in \(L^2\)-spaces.