Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains

Abstract

We establish the $L^p$ resolvent estimates for the Stokes operator in Lipschitz domains in $R^d$, $d\ge 3$ for $|\frac{1}{p}-1/2|<\frac{1}{2d}+\epsilon$. The result, in particular, implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in $L^p$ for $(3/2)-\varep < p< 3+ε$. This gives an affirmative answer to a conjecture of M. Taylor.

28 page. Minor revision was made regarding the definition of the Stokes operator in Lipschitz domains

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