Pointwise upper bounds for the solution of the Stokes equation on Lσ∞(Ω) and applications

Martin Bolkart, Matthias Georg Hieber

研究成果: Article

6 引用 (Scopus)

抄録

Consider the Stokes semigroup T defined on Lσ∞(Ω) where Ω⊂Rn, n≥3, denotes an exterior domain with smooth boundary. It is shown that T(z)u0 for u0∈Lσ∞(Ω) and z∈σθ with θ∈(0, π/2) satisfies pointwise estimates similar to the ones known for G(z)u0 where G denotes the Gaussian semigroup on Rn. In particular, T extends to a bounded analytic semigroup on Lσ∞(Ω) of angle π/2. Moreover, T(t) allows Lσ∞(Ω)-C2+α(Ω-) smoothing for every t>0 and the Stokes semigroups Tp and Tq on Lσp(Ω) and Lσq(Ω) are consistent for all p, q∈(1, ∞].

元の言語English
ページ(範囲)1678-1710
ページ数33
ジャーナルJournal of Functional Analysis
268
発行部数7
DOI
出版物ステータスPublished - 2015 4 1
外部発表Yes

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Stokes Equations
Semigroup
Upper bound
Stokes
Denote
Analytic Semigroup
Pointwise Estimates
Exterior Domain
Smoothing
Angle

ASJC Scopus subject areas

  • Analysis

これを引用

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title = "Pointwise upper bounds for the solution of the Stokes equation on Lσ∞(Ω) and applications",
abstract = "Consider the Stokes semigroup T∞ defined on Lσ∞(Ω) where Ω⊂Rn, n≥3, denotes an exterior domain with smooth boundary. It is shown that T∞(z)u0 for u0∈Lσ∞(Ω) and z∈σθ with θ∈(0, π/2) satisfies pointwise estimates similar to the ones known for G(z)u0 where G denotes the Gaussian semigroup on Rn. In particular, T∞ extends to a bounded analytic semigroup on Lσ∞(Ω) of angle π/2. Moreover, T∞(t) allows Lσ∞(Ω)-C2+α(Ω-) smoothing for every t>0 and the Stokes semigroups Tp and Tq on Lσp(Ω) and Lσq(Ω) are consistent for all p, q∈(1, ∞].",
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AU - Bolkart, Martin

AU - Hieber, Matthias Georg

PY - 2015/4/1

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N2 - Consider the Stokes semigroup T∞ defined on Lσ∞(Ω) where Ω⊂Rn, n≥3, denotes an exterior domain with smooth boundary. It is shown that T∞(z)u0 for u0∈Lσ∞(Ω) and z∈σθ with θ∈(0, π/2) satisfies pointwise estimates similar to the ones known for G(z)u0 where G denotes the Gaussian semigroup on Rn. In particular, T∞ extends to a bounded analytic semigroup on Lσ∞(Ω) of angle π/2. Moreover, T∞(t) allows Lσ∞(Ω)-C2+α(Ω-) smoothing for every t>0 and the Stokes semigroups Tp and Tq on Lσp(Ω) and Lσq(Ω) are consistent for all p, q∈(1, ∞].

AB - Consider the Stokes semigroup T∞ defined on Lσ∞(Ω) where Ω⊂Rn, n≥3, denotes an exterior domain with smooth boundary. It is shown that T∞(z)u0 for u0∈Lσ∞(Ω) and z∈σθ with θ∈(0, π/2) satisfies pointwise estimates similar to the ones known for G(z)u0 where G denotes the Gaussian semigroup on Rn. In particular, T∞ extends to a bounded analytic semigroup on Lσ∞(Ω) of angle π/2. Moreover, T∞(t) allows Lσ∞(Ω)-C2+α(Ω-) smoothing for every t>0 and the Stokes semigroups Tp and Tq on Lσp(Ω) and Lσq(Ω) are consistent for all p, q∈(1, ∞].

KW - Bounded analytic semigroups

KW - Exterior domain

KW - L estimates for Stokes equation

KW - Pointwise bounds

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