Long - time asymptotics of the Navier - Stokes equation in R 2 and R 3 Thierry
نویسنده
چکیده
Understanding the long-time evolution of fluid motions is facilitated by studying the coherent structures of the flow. From an experimental perspective this has long been recognized since visualizations of complicated flows often exhibit very obvious structures. Some of the most commonly observed structures are vortices. These vortices may appear initially through some instability in an underlying steady flow and then persist even after the flow becomes turbulent.
منابع مشابه
Invariant manifolds and the long - time asymptotics of the Navier - Stokes and vorticity equations on R 2
We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R2 and show that these manifolds control the long-time behavior of the solutions. This gives geometric insight into the existing results on the asymptotics of such solutions and also allows one to extend those results in a number of ways.
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We construct nite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R 2 and show that these manifolds control the long-time behavior of the solutions. This gives geometric insight into the existing results on the asymptotics of such solutions and also allows one to extend those results in a number of ways.
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We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R2 and show that these manifolds control the long-time behavior of the solutions. This gives geometric insight into the existing results on the asymptotics of such solutions and also allows one to extend those results in a number of ways.
متن کاملLong-time asymptotics of the Navier-Stokes and vorticity equations on R(3).
We use the vorticity formulation to study the long-time behaviour of solutions to the Navier-Stokes equation on R(3). We assume that the initial vorticity is small and decays algebraically at infinity. After introducing self-similar variables, we compute the long-time asymptotics of the rescaled vorticity equation up to second order. Each term in the asymptotics is a self-similar divergence-fre...
متن کاملLong-time asymptotics of the Navier-Stokes and vorticity equations on R
We use the vorticity formulation to study the long-time behavior of solutions to the Navier-Stokes equation on R3. We assume that the initial vorticity is small and decays algebraically at infinity. After introducing self-similar variables, we compute the long-time asymptotics of the rescaled vorticity equation up to second order. Each term in the asymptotics is a self-similar divergence-free v...
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تاریخ انتشار 2005