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 |
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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 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics