Long-time asymptotics of the Navier-Stokes and vorticity equations on ℝ3

@article{Gallay2002LongtimeAO,
  title={Long-time asymptotics of the Navier-Stokes and vorticity equations on ℝ3},
  author={T. Gallay and Eugene Wayne},
  journal={Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
  year={2002},
  volume={360},
  pages={2155 - 2188}
}
  • T. Gallay, Eugene Wayne
  • Published 2002
  • Mathematics, Medicine
  • Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
We use the vorticity formulation to study the long–time behaviour 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 vector field with Gaussian decay at infinity, and the coefficients in the expansion can be determined… Expand
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  • 47
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  • 154
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References

SHOWING 1-10 OF 53 REFERENCES
Asymptotic behavior for the vorticity equations in dimensions two and three
  • 62
  • PDF
Asymptotic Profiles of Nonstationary Incompressible Navier-Stokes Flows in the Whole Space
  • 68
  • Highly Influential
  • PDF
Scaling Variables and Asymptotic Expansions in Damped Wave Equations
  • 77
Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R2
  • 175
  • Highly Influential
  • PDF
Large-time behavior in incompressible Navier-Stokes equations
  • 41
  • PDF
On the localization of symmetric and asymmetric solutions of the Navier–Stokes equations in Rn
  • 42
Lower bounds of rates of decay for solutions to the Navier-Stokes equations
  • 157
  • PDF
...
1
2
3
4
5
...