Existence, uniqueness and Lq-estimates for the stokes problem in an exterior domain

Galdi, Giovanni P.; Simader, Christian G.

doi:10.1007/bf02384076

Cited by 116 publications

(61 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result is regarded as a generalization of [4], [22], [30], [31] in the usual case o ¼ 0, since the restriction on the exponent q is the same. Since the case q ¼ 3=2ð¼ n=2Þ needed to estimate the nonlinearity u Á 'u is missing in [28], an L q theory does not help to solve the nonlinear problem (1.2), (1.3).…”

Section: ð1:7þmentioning

confidence: 97%

Stationary Navier-Stokes Flow Around a Rotating Obstacle

Farwig

Hishida

2007

View full text Add to dashboard Cite

Abstract. Consider a viscous incompressible fluid filling the whole 3-dimensional space exterior to a rotating body with constant angular velocity o. By using a coordinate system attached to the body, the problem is reduced to an equivalent one in a fixed exterior domain. The reduced equation involves the crucial drift operator ðo5xÞ Á ', which is not subordinate to the usual Stokes operator. This paper addresses stationary flows to the reduced problem with an external force f ¼ div F , that is, time-periodic flows to the original one. Generalizing previous results of G. P. Galdi [19] we show the existence of a unique solution ð'u; pÞ in the class L 3=2; y when both F A L 3=2; y and o are small enough; here L 3=2; y is the weak-L 3=2 space.

show abstract

Section: ð1:7þmentioning

confidence: 97%

Stationary Navier-Stokes Flow Around a Rotating Obstacle

Farwig

Hishida

2007

View full text Add to dashboard Cite

show abstract

“…8 < : ð1:2Þ was investigated by several authors [3,6,8], and they showed that for every F A L q ðWÞ there exists a unique solution of (1.2) in the class 'u A L q ðWÞ if and only if 3=2 < q < 3. The nonlinear problem (1.1), however, requires q ¼ 3=2 to estimate the nonlinearity.…”

Section: > > > < > > > : ð1:1þmentioning

confidence: 99%

Uniqueness of Steady Navier-Stokes Flows in Exterior Domains

Nakatsuka

2013

View full text Add to dashboard Cite

Abstract. We consider the uniqueness of stationary solutions to the Navier-Stokes equation in 3-dimensional exterior domains within the class u A L 3; y with 'u A L 3=2; y , where L 3; y and L 3=2; y are the Lorentz spaces. It is shown that if solutions u and v satisfy the conditions that u is small in L 3; y and v A L 3 þ L y , then u ¼ v. The proof relies upon the regularity theory for the perturbed Stokes equation.

show abstract

“…II, Chapters. 9, 10), [27], [31], [32], [35], [40], [41], [47], [56]) and, more recently, also for the compressible case (see [37], [38], [39], [36], [44], [45], [48]). In general, exterior fluid dynamical problems present further essential difficulties compared to the interior ones (bounded domains).…”

Section: Introductionmentioning

confidence: 99%

“…In this respect, there has been an intensive study for corresponding linearized systems (that is Stokes-like, if v ∞ = 0, or Oseen-like, if v ∞ ≡ 0), cf. Galdi and Simader [27], Galdi [23], [24], Kozono and Sohr [32], Borchers, Miyakawa [8]. However, these studies have revealed, so far, insufficient to produce results for the nonlinear theory, at least when v ∞ = 0, because of Italian C.N.R.…”

Section: Introductionmentioning

confidence: 99%