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.
ASJC Scopus subject areas
- 数学 (全般)