Math @ Duke

Publications [#139011] of JianGuo Liu
Papers Published
 J.G. Liu, Jie Liu and R. Pego, Estimates on the Stokes pressure by partitioning the energy of harmonic functions,
in Kyoto Conference on the NavierStokes equations and their Applications, edited by Y. Giga, H. Kozono, H. Okamoto and Y. Shibta
(2007),
pp. 251270, Kyoto Univ.
(last updated on 2007/12/07)
Abstract: We show that in a tubular domain with sufficiently small width, the normal and tangential gradients of a harmonic
function have almost the same L2 norm. This estimate yields a sharp estimate of the pressure in terms of the viscosity
term in the NavierStokes equation with noslip boundary condition. By consequence, one can analyze the Navier
Stokes equations simply as a perturbed vector diffusion equation instead of as a perturbed Stokes system. As an
application, we describe a rather easy approach to establish a new isomorphism theorem for the nonhomogeneous
Stokes system.


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