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An application of homogenization techniques to population dynamics models
Global well-posedness of weak solutions for the Lagrangian averaged Navier-Stokes equations on bounded domains
| 1. | Department of Mathematics, University of California, Davis, CA 95616, United States |
We prove the global well-posedness of weak $H^1$ solutions for the case of no-slip boundary conditions in three dimensions, generalizing the periodic-box results of [8]. We make use of the new formulation of the LANS-$\alpha$ equations on bounded domains given in [20] and [14], which reveals the additional boundary conditions necessary to obtain well-posedness. The uniform estimates yield global attractors; the bound for the dimension of the global attractor in 3D exactly follows the periodic box case of [8]. In 2D, our bound is $\alpha$-independent and is similar to the bound for the global attractor for the 2D Navier-Stokes equations.
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