Je. Marsden et S. Shkoller, Global well-posedness for the Lagrangian averaged Navier-Stokes (LANS-alpha) equations on bounded domains, PHI T ROY A, 359(1784), 2001, pp. 1449-1468
Citations number
49
Categorie Soggetti
Multidisciplinary
Journal title
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
We prove the global well-posedness and regularity of the (isotropic) Lagran
gian averaged Navier-Stokes (LANS-alpha) equations on a three-dimensional b
ounded domain with a smooth boundary with no-slip boundary conditions for i
nitial data in the set (u is an element of H-s boolean AND H-0(1) / Au. = 0
on partial derivative Omega div u = 0), s is an element of [3: 5), where A
is the Stokes operator. As with the Navier-Stokes equations, one has parab
olic-type regularity; that is, the solutions instantaneously become space-t
ime smooth when the forcing is smooth (or zero).
The equations are an ensemble average of the Navier-Stokes equations over i
nitial data in an a-radius phase-space ball, and converge to the Navier-Sto
kes equations as alpha --> 0, We also show that classical solutions of the
LANS-alpha equations converge almost all in H-s for s is an element of (2.5
,3), to solutions of the inviscid equations (v = 0). called the Lagrangian
averaged Euler (LAE-alpha) equations, even on domains with boundary, for ti
me-intervals governed by the time of existence of solutions of the LAE=alph
a equations.