On analyticity of the    L  p   ‐Stokes semigroup for some non‐Helmholtz domains | Zendy

Bolkart Martin | Zendy; Giga Yoshikazu | Zendy; Miura TatsuHiko | Zendy; Suzuki Takuya | Zendy; Tsutsui Yohei | Zendy

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On analyticity of the L p ‐Stokes semigroup for some non‐Helmholtz domains

Author(s) -

Bolkart Martin,

Giga Yoshikazu,

Miura TatsuHiko,

Suzuki Takuya,

Tsutsui Yohei

Publication year - 2017

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201600016

Subject(s) - mathematics , semigroup , solenoidal vector field , domain (mathematical analysis) , projection (relational algebra) , helmholtz free energy , mathematical analysis , analytic semigroup , helmholtz equation , pure mathematics , boundary value problem , geometry , vector field , physics , algorithm , quantum mechanics

Consider the Stokes equations in a sector‐like C 3 domain Ω ⊂ R 2 . It is shown that the Stokes operator generates an analytic semigroup inL σ p ( Ω )for p ∈ [ 2 , ∞ ) . This includes domains where the L p ‐Helmholtz decomposition fails to hold. To show our result we interpolate results of the Stokes semigroup in V M O and L 2 by constructing a suitable non‐Helmholtz projection to solenoidal spaces.

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