Stationary Navier-Stokes Flow in Exterior Domains and Landau Solutions

Hishida, Toshiaki

doi:10.1007/978-3-319-10151-4_6-1

Cited by 2 publications

(2 citation statements)

References 53 publications

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“…In fact, the leading term is a Landau solution with label N when the body is at rest ( [43]), while it is another Landau solution with label (N • ω |ω| ) ω |ω| when the body is rotating with constant angular velocity ω = 0 but η = 0 (due to [11] and then refined by [10]). See also Galdi [15] and expository articles [22,35] by Galdi, Neustupa and the present author for more details. Similar asymptotic structure to what is mentioned above still holds even for time-periodic Navier-Stokes flows, that we are going to discuss in what follows, when the body is at rest or translating periodically along a constant direction, see Galdi and Kyed [21,Section 4.9].…”

Section: Introductionmentioning

confidence: 99%

Spatial Pointwise Behavior of Time-Periodic Navier–Stokes Flow Induced by Oscillation of a Moving Obstacle

Hishida

2022

J. Math. Fluid Mech.

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We study the spatial decay of time-periodic Navier–Stokes flow at the rate $$|x|^{-1}$$ | x | - 1 with/without wake structure in 3D exterior domains when a rigid body moves periodically in time. In this regime the existence of time-periodic solutions was established first in the 2006 paper by Galdi and Silvestre, however, with little information about spatial behavior at infinity so that uniqueness of solutions was not available. This latter issue has been addressed by Galdi, who has recently succeeded in construction of a unique time-periodic solution with spatial behavior mentioned above if translational and angular velocities of the body fulfill, besides smallness and regularity, either of the following assumptions: (i) translation or rotation is absent; (ii) both velocities are parallel to the same constant vector. This paper shows the existence of a unique time-periodic Navier–Stokes flow in the small with values in the weak-$$L^3$$ L 3 space and then deduces the desired pointwise decay of the solution under some condition on the rigid motion of the body, that covers the cases (i), (ii) mentioned above.

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Section: Introductionmentioning

confidence: 99%

Spatial Pointwise Behavior of Time-Periodic Navier–Stokes Flow Induced by Oscillation of a Moving Obstacle

Hishida

2022

J. Math. Fluid Mech.

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“…Indeed, it was proved by Miura and Tsai [13] that the leading term of point singularity like |x| −1 at x = 0 of the Navier-Stokes flow is also given by a Landau solution provided it is small enough. See Hishida [5] for a survey including stationary Navier-Stokes flows around a rotating body.…”

Section: Introductionmentioning

confidence: 99%

On bifurcation of self-similar solutions of the stationary Navier-Stokes equations

Kwon¹,

Tsai²

2020

Preprint

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Landau solutions are special solutions to the stationary incompressible Navier-Stokes equations in the three dimensional space excluding the origin. They are self-similar and axisymmetric with no swirl. In fact, any self-similar smooth solution must be a Landau solution. In the effort of extending this result to the one for the solution class with the pointwise scale-invariant bound |u(x)| ≤ C 0 |x| −1 for some C 0 > 0, we consider axisymmetric discretely self-similar solutions, and investigate the existence of such solution curve emanating from some Landau solution. We prove that the inclusion of the swirl component does not enhance the bifurcation and present numerical evidence of no bifurcation.

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Stationary Navier-Stokes Flow in Exterior Domains and Landau Solutions

Cited by 2 publications

References 53 publications

Spatial Pointwise Behavior of Time-Periodic Navier–Stokes Flow Induced by Oscillation of a Moving Obstacle

Spatial Pointwise Behavior of Time-Periodic Navier–Stokes Flow Induced by Oscillation of a Moving Obstacle

On bifurcation of self-similar solutions of the stationary Navier-Stokes equations

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