On nonstationary solutions of the Navier-Stokes equations in an exterior domain

Miyakawa, Tetsuro

doi:10.32917/hmj/1206133879

Cited by 170 publications

(87 citation statements)

References 17 publications

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“…For the proof, see Fujiwara and Morimoto [8], Miyakawa [28] and Simader and Sohr [33]. Let P p denote the projection operator from (L p (Ω)) n onto L p σ (Ω) along G p (Ω).…”

Section: Resultsmentioning

confidence: 99%

The Navier-Stokes equations in the weak- $L^n$ space with time-dependent external force

2000

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We consider the Navier-Stokes equations with time-dependent external force, either in the whole time or in positive time with initial data, with domain either the whole space, the half space or an exterior domain of dimension n ≥ 3. We give conditions on the external force sufficient for the unique existence of small solutions in the weak-L n space bounded for all time.In particular, this result gives sufficient conditions for the unique existence and the stability of small time-periodic solutions or almost periodic solutions. This result generalizes the previous result on the unique existence and the stability of small stationary solutions in the weak-L n space with time-independent external force.

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“…For the proof, see Fujiwara and Morimoto [8], Miyakawa [28] and Simader and Sohr [33]. Let P p denote the projection operator from (L p (Ω)) n onto L p σ (Ω) along G p (Ω).…”

Section: Resultsmentioning

confidence: 99%

The Navier-Stokes equations in the weak- $L^n$ space with time-dependent external force

2000

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“…We do answer this question in this paper neither for the operator A 0 γ nor for the more general operator A ω γ . The Oseen operator A 0 γ generates an analytic semigroup, see T. Miyakawa [22]. Therefore the operator (−A 0 γ ) is sectorial, see D. Henry [14], p. 20-21.…”

Section: The Oseen Operatormentioning

confidence: 99%

On the Spectrum of an Oseen-Type Operator Arising from Flow past a Rotating Body

Farwig

Neustupa

2008

Integr. equ. oper. theory

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We present the description of the spectrum of a linear perturbed Oseen-type operator which arises from equations of motion of a viscous incompressible fluid in the exterior of a rotating compact body. Considering the operator in the function space L 2 σ (Ω) we prove that the essential spectrum consists of an infinite set of overlapping parabolic regions in the left half-plane of the complex plane. Our approach is based on a reduction to invariant closed subspaces of L 2 σ (Ω) and on a Fourier series expansion with respect to an angular variable in a cylindrical coordinate system attached to the axis of rotation. Mathematics Subject Classification (2000). Primary 35Q35; Secondary 35P99, 76D07.

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“…The Helmholtz decompositon was proved by Fujiwara and Morimoto [7], Miyakawa [17] and Simader and Sohr [23] (cf. Galdi [9]).…”

Section: Y Enomoto and Y Shibata Jmfmmentioning

confidence: 99%

On the Rate of Decay of the Oseen Semigroup in Exterior Domains and its Application to Navier–Stokes Equation

Enomoto

Shibata

2005

J. math. fluid mech.

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We prove Lp-Lq estimates of the Oseen semigroup in n-dimensional exterior domains (n 3), which refine and improve those obtained by Kobayashi and Shibata [15]. As an application, we give a globally in time stability theory for the stationary Navier-Stokes flow whose velocity at infinity is a non-zero constant vector. We thus extend the result of Shibata [21]. In particular, we find an optimal rate of convergence of solutions of the non-stationary problem to those of the corresponding stationary problem. (2000). 35B40, 35M20, 73B30. Mathematics Subject Classification

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On nonstationary solutions of the Navier-Stokes equations in an exterior domain

Cited by 170 publications

References 17 publications

The Navier-Stokes equations in the weak- $L^n$ space with time-dependent external force

The Navier-Stokes equations in the weak- $L^n$ space with time-dependent external force

On the Spectrum of an Oseen-Type Operator Arising from Flow past a Rotating Body

On the Rate of Decay of the Oseen Semigroup in Exterior Domains and its Application to Navier–Stokes Equation

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