Inviscid limit for damped and driven incompressible Navier-Stokes equations in ℝ2

P. Constantin; F. Ramos

doi:10.1007/s00220-007-0310-7

Inviscid limit for damped and driven incompressible Navier-Stokes equations in ℝ²

P. Constantin, F. Ramos

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in ℝ. We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstrophy balance.

Original language	English (US)
Pages (from-to)	529-551
Number of pages	23
Journal	Communications In Mathematical Physics
Volume	275
Issue number	2
DOIs	https://doi.org/10.1007/s00220-007-0310-7
State	Published - Oct 2007
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-007-0310-7

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abstract = "We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in ℝ. We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstrophy balance.",

author = "P. Constantin and F. Ramos",

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AU - Ramos, F.

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N2 - We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in ℝ. We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstrophy balance.

AB - We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in ℝ. We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstrophy balance.

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Inviscid limit for damped and driven incompressible Navier-Stokes equations in ℝ²

Abstract

All Science Journal Classification (ASJC) codes

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