Levermore, C. David; Sammartino, Marco A shallow water model with eddy viscosity for basins with varying bottom topography. (English) Zbl 0999.76033 Nonlinearity 14, No. 6, 1493-1515 (2001). Summary: We consider the motion of an incompressible fluid confined to a shallow basin with varying bottom topography. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three-dimensional eddy viscosity model plays a critical role in ensuring that the resulting shallow water model dissipates energy. Cited in 2 ReviewsCited in 22 Documents MSC: 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76D05 Navier-Stokes equations for incompressible viscous fluids 76D27 Other free boundary flows; Hele-Shaw flows 35Q30 Navier-Stokes equations Keywords:energy dissipation; three-dimensional incompressible Navier-Stokes equations; anisotropic stress tensor; shallow basin; varying bottom topography; three-dimensional anisotropic eddy viscosity model; two-dimensional shallow water model; global regularity PDFBibTeX XMLCite \textit{C. D. Levermore} and \textit{M. Sammartino}, Nonlinearity 14, No. 6, 1493--1515 (2001; Zbl 0999.76033) Full Text: DOI