Backward uniqueness and unique continuation for solutions to the Navier- Stokes equations on an exterior domain
Using the results obtained by \textit{J. Serrin} [Nonlinear Prob., Proc. Sympos. Madison, 69-98 (1963; Zbl 0115.085)], \textit{D. E. Edmunds} [Arch. Ration. Mech. Anal. 14, 171-176 (1963; Zbl 0126.423)], \textit{S. Rionero} and \textit{G. P. Galdi} [Arch. Ration. Mech. Anal. 62, 295-301 (1976; Zbl 0351.35070)], the author shows the backward uniqueness of the solution of the Navier-Stokes equations on a spatially unbounded domain exterior to a compact set in \({\mathbb{R}}^ 3\). This result is established under weaker decay assumptions than those required in Edmund's analysis. The asymptotic behaviour (the determination of the rate of decay in time) of the same Navier-Stokes equations is also developed.
spatially unbounded domain exterior to a compact set
scientific article; zbMATH DE number 3870821