We study the long time behavior of a shallow water model introduced by Levermore and Sammartino to describe the motion of a viscous incompressible fluid confined in a basin with topography. Here we prove the existence of a global attractor and give an estimate on its Hausdorff and fractal dimension.
Sammartino, M., Sciacca, V. (2002). LONG TIME BEHAVIOR OF A SHALLOW WATER MODEL FOR A BASIN WITH VARYING BOTTOM TOPOGRAPHY. In "WASCOM 2001"---11th Conference on Waves and Stability in Continuous Media (pp.515-520). SINGAPORE : WORLD SCIENTIFIC PUBL CO PTE LTD [10.1142/9789812777331_0063].
LONG TIME BEHAVIOR OF A SHALLOW WATER MODEL FOR A BASIN WITH VARYING BOTTOM TOPOGRAPHY
SAMMARTINO, Marco Maria Luigi;SCIACCA, Vincenzo
2002-01-01
Abstract
We study the long time behavior of a shallow water model introduced by Levermore and Sammartino to describe the motion of a viscous incompressible fluid confined in a basin with topography. Here we prove the existence of a global attractor and give an estimate on its Hausdorff and fractal dimension.
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