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- W2949766029 abstract "We consider the steady-state Navier-Stokes equation in the whole space $mathbb{R}^3$ driven by a forcing function $f$. The class of source functions $f$ under consideration yield the existence of at least one solution with finite Dirichlet integral ($|nabla U|_2<infty$). Under the additional assumptions that $f$ is absent of low modes and the ratio of $f$ to viscosity is sufficiently small in a natural norm we construct solutions which have finite energy (finite $L^2$ norm). These solutions are unique among all solutions with finite energy and finite Dirichlet integral. The constructed solutions are also shown to be stable in the following sense: If $U$ is such a solution then any viscous, incompressible flow in the whole space, driven by $f$ and starting with finite energy, will return to $U$." @default.
- W2949766029 created "2019-06-27" @default.
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- W2949766029 date "2007-11-27" @default.
- W2949766029 modified "2023-09-27" @default.
- W2949766029 title "Existence and Stability of Steady-State Solutions with Finite Energy for the Navier-Stokes equation in the Whole Space" @default.
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