|
Center for Nonlinear Analysis
CNA Home
People
Seminars
Publications
Workshops and Conferences
CNA Working Groups
CNA Comments Form
Summer Schools
Summer Undergraduate Institute
PIRE
Cooperation
Graduate Topics Courses
SIAM Chapter Seminar
Positions
Contact |
Publication 09-CNA-20
On Optimal Estimates for the Laplace-Leray Commutator in Planar Domains with Corners Elaine Cozzi Robert L. Pego Abstract: 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 in Get the paper in its entirety as |
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.