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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.