Marsden, Jerrold E. and Shkoller, Steve (2001) Global wellposedness for the Lagrangian averaged NavierStokes (LANSα) equations on bounded domains. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 359 (1784). pp. 14491468. ISSN 1364503X . http://resolver.caltech.edu/CaltechAUTHORS:20101005112356720

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Abstract
We prove the global wellposedness and regularity of the (isotropic) Lagrangian averaged NavierStokes (LANSα) equations on a threedimensional bounded domain with a smooth boundary with noslip boundary conditions for initial data in the set {u ∈ H^s ∩ H_0^1 Au = 0 on ∂Ω, div u = 0}, s ∈ [3,5), where A is the Stokes operator. As with the NavierStokes equations, one has parabolictype regularity; that is, the solutions instantaneously become spacetime smooth when the forcing is smooth (or zero). The equations are an ensemble average of the NavierStokes equations over initial data in an αradius phasespace ball, and converge to the NavierStokes equations as α → 0. We also show that classical solutions of the LANSα equations converge almost all in H^s for s ∈ (2:5; 3), to solutions of the inviscid equations (v = 0), called the Lagrangian averaged Euler (LAEα) equations, even on domains with boundary, for timeintervals governed by the time of existence of solutions of the LAEα equations.
Item Type:  Article  

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Additional Information:  © 2001 The Royal Society. This is one article from the Discussion Meeting Issue ‘Topological methods in the physical sciences’ organized by V. I. Arnold, J. W. Bruce, H. K. Moffatt and R. B. Pelz.  
Subject Keywords:  NavierStokes; averaging; largescale row; Euler equations; turbulence  
Record Number:  CaltechAUTHORS:20101005112356720  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20101005112356720  
Official Citation:  Marsden, J. E. and S. Shkoller (2001). "Global well–posedness for the Lagrangian averaged Navier–Stokes (LANS–α) equations on bounded domains." Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 359(1784): 14491468.  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  20305  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  16 Nov 2010 23:46  
Last Modified:  20 Nov 2014 23:42 
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