Large Time Behavior of the Navier–Stokes Flow

Brandolese, Lorenzo; Schonbek, María E.

doi:10.1007/978-3-319-10151-4_11-1

Cited by 2 publications

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References 149 publications

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“…This constrasts with the case ǫ = 0 of the Navier-Stokes equations: indeed, solutions of the Navier-Stokes equations are known to decay as u(t) 2 ∼ t −(n+2)/4 as soon as u 0 is well localized, see [17], and sometimes even at faster rates (e.g., under appropriate symmetries). See contribution [3] for an up-to-date review of decay issues for the Navier-Stokes flows. Remark 3.2.…”

Section: The Above Conclusion Holds In Any Dimensionmentioning

confidence: 99%

On a non-solenoidal approximation to the incompressible Navier-Stokes equations

Brandolese

2017

J. London Math. Soc.

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We establish an asymptotic profile that sharply describes the behavior as t→∞ for solutions to a non‐solenoidal approximation of the incompressible Navier–Stokes equations introduced by Temam. The solutions of Temam's model are known to converge to the corresponding solutions of the classical Navier–Stokes, for example, in L loc 3false(double-struckR+×double-struckR3false), provided ε→0, where ε>0 is the physical parameter related to the artificial compressibility term. However, we show that such model is no longer a good approximation of Navier–Stokes for large times: indeed, its solutions can decay much slower as t→∞ than the corresponding solutions of Navier–Stokes.

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Section: The Above Conclusion Holds In Any Dimensionmentioning

confidence: 99%

On a non-solenoidal approximation to the incompressible Navier-Stokes equations

Brandolese

2017

J. London Math. Soc.

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Stability of a two‐dimensional stationary rotating flow in an exterior cylinder

Higaki

2022

Mathematische Nachrichten

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We investigate the stability of an exact stationary flow in an exterior cylinder. The horizontal velocity is the two-dimensional rotating flow in an exterior disk with a critical spatial decay, for which the 𝐿 2 stability is known under smallness conditions. We prove its stability property for three-dimensional perturbations although the Hardy type inequalities are absent as in the twodimensional case. The proof uses a large time estimate for the linearized equations exhibiting different behaviors in the Fourier modes, namely, the standard 𝐿 2 -𝐿 𝑞 decay of the two-dimensional mode and an exponential decay of the three-dimensional modes.

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Large Time Behavior of the Navier–Stokes Flow

Cited by 2 publications

References 149 publications

On a non-solenoidal approximation to the incompressible Navier-Stokes equations

On a non-solenoidal approximation to the incompressible Navier-Stokes equations

Stability of a two‐dimensional stationary rotating flow in an exterior cylinder

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