Asymptotics of Small Exterior Navier-Stokes Flows with Non-Decaying Boundary Data
We prove the existence of unique solutions for the 3D incompressible Navier-Stokes equations in an exterior domain with small boundary data which do not necessarily decay in time. As a corollary, the existence of unique small time-periodic solutions is shown. We next show that the spatial asymptotic...
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| Veröffentlicht in: | Communications in partial differential equations 2012-10, Vol.37 (10), p.1717-1753 |
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| container_title | Communications in partial differential equations |
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| creator | Kang, Kyungkuen Miura, Hideyuki Tsai, Tai-Peng |
| description | We prove the existence of unique solutions for the 3D incompressible Navier-Stokes equations in an exterior domain with small boundary data which do not necessarily decay in time. As a corollary, the existence of unique small time-periodic solutions is shown. We next show that the spatial asymptotics of the periodic solution is given by the same Landau solution at all times. Lastly we show that if the boundary datum is time-periodic and the initial datum is asymptotically self-similar, then the solution converges to the sum of a time-periodic vector field and a forward self-similar vector field as time goes to infinity. |
| doi_str_mv | 10.1080/03605302.2012.708082 |
| format | Article |
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| ispartof | Communications in partial differential equations, 2012-10, Vol.37 (10), p.1717-1753 |
| issn | 0360-5302 1532-4133 |
| language | eng |
| recordid | cdi_proquest_journals_1151593776 |
| source | Taylor & Francis:Master (3349 titles) |
| subjects | Discretely self-similar Exterior domain Fluid dynamics Landau solution Navier-Stokes equations Spatial asymptotics Stability Studies Time asymptotics Time-periodic |
| title | Asymptotics of Small Exterior Navier-Stokes Flows with Non-Decaying Boundary Data |
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