Asymptotics of solutions to the Navier-Stokes system in exterior domains

作者：Iftimie Dragos^*; Karch Grzegorz; Lacave Christophe

来源：Journal of the London Mathematical Society-Second Series, 2014, 90(3): 785-806.

DOI：10.1112/jlms/jdu052

We consider the incompressible Navier-Stokes equations with the Dirichlet boundary condition in an exterior domain of R-n with n %26gt;= 2. We compare the long-time behaviour of solutions to this initial-boundary value problem with the long-time behaviour of solutions of the analogous Cauchy problem in the whole space R-n. We find that the long-time asymptotics of solutions to both problems coincide either in the case of small initial data in the weak L-n-space or for a certain class of large initial data.

• 出版日期2014-12