Existence and uniqueness of time-periodic physically reasonable Navier-Stokes flow past a body

Let Ω be a three-dimensional exterior domain of class C^sup 2,α^ , 0

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Veröffentlicht in:Archive for rational mechanics and analysis 2004-05, Vol.172 (3), p.363-406
Hauptverfasser: GALDI, Giovanni P, SOHR, Hermann
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SOHR, Hermann
description Let Ω be a three-dimensional exterior domain of class C^sup 2,α^ , 0
doi_str_mv 10.1007/s00205-004-0306-9
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Assume that a Navier-Stokes liquid is moving in Ω under the action of a body force F that is time-periodic of period T , and that the velocity of the liquid is zero at spatial infinity. In this paper we show that, if F satisfies suitable conditions, and its norm, in appropriate function spaces, is sufficiently small, there is at least one time-periodic strong solution. Furthermore, the velocity field v of such a solution decays to zero for large |x | as |x |^sup -1^ and its spatial gradient decays as |x |^sup -2^ , both uniformly in time. In addition, the pressure p decays like |x |^sup -2^ and its gradient like |x |^sup -3^ , for almost all t [0,T ]. In the special case where F is time-independent, these solutions are also time-independent and coincide with Finn's ''physically reasonable'' solutions [4]. 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Assume that a Navier-Stokes liquid is moving in Ω under the action of a body force F that is time-periodic of period T , and that the velocity of the liquid is zero at spatial infinity. In this paper we show that, if F satisfies suitable conditions, and its norm, in appropriate function spaces, is sufficiently small, there is at least one time-periodic strong solution. Furthermore, the velocity field v of such a solution decays to zero for large |x | as |x |^sup -1^ and its spatial gradient decays as |x |^sup -2^ , both uniformly in time. In addition, the pressure p decays like |x |^sup -2^ and its gradient like |x |^sup -3^ , for almost all t [0,T ]. In the special case where F is time-independent, these solutions are also time-independent and coincide with Finn's ''physically reasonable'' solutions [4]. 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subjects Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Numerical approximation and analysis
Ordinary and partial differential equations, boundary value problems
Physics
Studies
title Existence and uniqueness of time-periodic physically reasonable Navier-Stokes flow past a body
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