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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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Joel Avrin. Global existence and regularity for the Lagrangian averaged Navier-Stokes equations with initial data in $H^{1//2}$. Communications on Pure & Applied Analysis, 2004, 3 (3) : 353-366. doi: 10.3934/cpaa.2004.3.353 |
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T. Tachim Medjo. Averaging of a 3D Lagrangian averaged Navier-Stokes-$\alpha$ model with oscillating external forces. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1281-1305. doi: 10.3934/cpaa.2011.10.1281 |
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Hermenegildo Borges de Oliveira. Anisotropically diffused and damped Navier-Stokes equations. Conference Publications, 2015, 2015 (special) : 349-358. doi: 10.3934/proc.2015.0349 |
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Hyukjin Kwean. Kwak transformation and Navier-Stokes equations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 433-446. doi: 10.3934/cpaa.2004.3.433 |
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