Date of Original Version

6-2010

Type

Article

Rights Management

Published by the American Mathematical Society

Abstract or Description

For smooth domains, Liu et al. (Comm. Pure Appl. Math. 60: 1443-1487, 2007) used optimal estimates for the commutator of the Laplacian and the Leray projection operator to establish well-posedness of an extended Navier-Stokes dynamics. In their work, the pressure is not determined by incompressibility, but rather by a certain formula involving the Laplace-Leray commutator. A key estimate of Liu et al. controls the commutator strictly by the Laplacian L2 in norm at leading order. In this paper we show that this strict control fails in a large family of bounded planar domains with corners. However, when the domain is an infinite cone, we find that strict control may be recovered in certain power-law weighted norms

DOI

10.1090/S0002-9939-2010-10613-5

Included in

Mathematics Commons

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Published In

Proceedings of the American Mathematical Society, 139, 1691-1706.