Asymptotic behavior for the Navier-Stokes equations in 2D exterior domains (Q860790)

The authors study \(L^p\) spatial-temporal decay rates of incompressible flow in an 2D exterior domain. If the domain has a boundary, ther is not enough information on the pressure term near the boundary. To overcome this difficulty they adopt ideas of C. He and H.-O. Bae. To obtain a spatial decay rate estimate, the authors first extend the temporal decay rate result for the Navier-Stokes solutions to the whole \(L^p\) space when the initial velocity is in \(L^2_\sigma\cap L^r\), \(1<r\leq q<\infty\) \((1< r<q =\infty)\).