Abstract
Consider a domain ω ⊂ℝ n with possibly non compact but uniform C 3-boundary and assume that the Helmholtz projection P exists on L p(W) for some 1 <p <∞. It is shown that the Stokes operator in L p(W) generates an analytic semigroup on L σ p(ω) admitting maximal L q-L p-regularity. Moreover, for u 0 ε L σ p(W) there exists a unique local mild solution to the Navier-Stokes equations on domains of this form provided p > n.
Original language | English |
---|---|
Pages (from-to) | 75-100 |
Number of pages | 26 |
Journal | Journal fur die Reine und Angewandte Mathematik |
Issue number | 669 |
DOIs | |
Publication status | Published - 2012 Aug |
Externally published | Yes |
Fingerprint
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Weak Neumann implies Stokes. / Geissert, Matthias; Heck, Horst; Hieber, Matthias Georg; Sawada, Okihiro.
In: Journal fur die Reine und Angewandte Mathematik, No. 669, 08.2012, p. 75-100.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Weak Neumann implies Stokes
AU - Geissert, Matthias
AU - Heck, Horst
AU - Hieber, Matthias Georg
AU - Sawada, Okihiro
PY - 2012/8
Y1 - 2012/8
N2 - Consider a domain ω ⊂ℝ n with possibly non compact but uniform C 3-boundary and assume that the Helmholtz projection P exists on L p(W) for some 1 p(W) generates an analytic semigroup on L σ p(ω) admitting maximal L q-L p-regularity. Moreover, for u 0 ε L σ p(W) there exists a unique local mild solution to the Navier-Stokes equations on domains of this form provided p > n.
AB - Consider a domain ω ⊂ℝ n with possibly non compact but uniform C 3-boundary and assume that the Helmholtz projection P exists on L p(W) for some 1 p(W) generates an analytic semigroup on L σ p(ω) admitting maximal L q-L p-regularity. Moreover, for u 0 ε L σ p(W) there exists a unique local mild solution to the Navier-Stokes equations on domains of this form provided p > n.
UR - http://www.scopus.com/inward/record.url?scp=84870214473&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84870214473&partnerID=8YFLogxK
U2 - 10.1515/CRELLE.2011.150
DO - 10.1515/CRELLE.2011.150
M3 - Article
AN - SCOPUS:84870214473
SP - 75
EP - 100
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 669
ER -