L p -theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Geißert, Matthias; Heck, Horst; Hieber, Matthias

doi:10.1515/crelle.2006.051

Cited by 63 publications

(74 citation statements)

References 19 publications

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“…As for the nonstationary problem, the existence of global weak solutions is proved by Borchers [2], and the unique existence of time-local regular solutions is shown by Hishida [20] and Geissert, Heck, and Hieber [18], while the global strong solutions for small data are obtained by Galdi and Silvestre [15]. The spectrum of the linear operator arising in this problem is studied by Farwig and Neustupa [10]; see also the linear analysis by Hishida [21].…”

Section: Theorem 13 There Exists a Positive Constant δ Such That If mentioning

confidence: 99%

See 1 more Smart Citation

On Stability of Steady Circular Flows in a Two-Dimensional Exterior Disk

Maekawa

2017

Arch Rational Mech Anal

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We study the stability of some exact stationary solutions to the two-dimensional Navier-Stokes equations in an exterior domain to the unit disk. These stationary solutions are known as a simple model of the flow around a rotating obstacle, while their stability has been open due to the difficulty arising from their spatial decay in a scale-critical order. In this paper we affirmatively settle this problem for small solutions. That is, we will show that if these exact solutions are small enough then they are asymptotically stable with respect to small L 2 perturbations.Keywords Navier-Stokes equations · two-dimensional exterior flows · scale-criticality · stability of stationary flows · flow around a rotating obstacle

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Section: Theorem 13 There Exists a Positive Constant δ Such That If mentioning

confidence: 99%

“…The identities (18) and (19) are straightforward and we omit the proof. The identity (20) follows from…”

Section: Vector Fields In the Polar Coordinatesmentioning

confidence: 99%

On Stability of Steady Circular Flows in a Two-Dimensional Exterior Disk

Maekawa

2017

Arch Rational Mech Anal

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“…In order to prove Theorem 3.1 we make use of the following lemma on iterated convolutions proved in [3]. …”

Section: P -L Q Smoothing Properties Of E Tlωmentioning

confidence: 99%

“…[6], [5], [3]. Whereas the situation for L p (R n ), equipped either with the Lebesgue measure or the invariant measure, can be regarded as fairly well understood, this is not the case for exterior domains.…”

Section: Introductionmentioning

confidence: 99%

The Ornstein-Uhlenbeck semigroup in exterior domains

et al. 2005

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“…On the existence, uniqueness and regularity of solutions of (1), there are many papers, such as [1][2][3][4][5][6][7][8] and references therein. However, few results about the numerical analysis are developed.…”

Section: Introductionmentioning

confidence: 99%

The boundary integral method for the steady rotating Navier–Stokes equations in exterior domain (I): the existence of solution

2009

Nonlinear Differ. Equ. Appl.

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Abstract. In this paper, we apply the boundary integral method to the steady rotating Navier-Stokes equations in exterior domain. Introducing some open ball which decomposes the exterior domain into a finite domain and a infinite domain, we obtain a coupled problem by the steady rotating Navier-Stokes equations in finite domain and a boundary integral equation without using the artificial boundary condition. For the coupled problem, we show the existence of solution in a convex set. Mathematics Subject Classification (2000). 76M15, 76U05.

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L p -theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Abstract: Abstract. In this paper we describe two recent approaches for the L p -theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle.

Cited by 63 publications

References 19 publications

On Stability of Steady Circular Flows in a Two-Dimensional Exterior Disk

On Stability of Steady Circular Flows in a Two-Dimensional Exterior Disk

The Ornstein-Uhlenbeck semigroup in exterior domains

The boundary integral method for the steady rotating Navier–Stokes equations in exterior domain (I): the existence of solution

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