The 2015 AMMCS-CAIMS Congress

Interdisciplinary AMMCS Conference Series

Waterloo, Ontario, Canada | June 7-12, 2015

AMMCS-CAIMS 2015 Semi-Plenary Talk

Conservation laws of fluid flow on Riemannian manifolds

Stephen Anco (Brock University)

All local conservation laws of kinematic type on moving domains and moving surfaces for inviscid compressible fluid flow on curved Riemannian manifolds are derived. In particular, any such conservation laws will be found that hold only for (1) special dimensions of the manifold or the surface; (2) special conditions on the geometry of the manifold or the surface; (3) special equations of state. Importantly, the general form of these kinematic conservation laws will be allowed to depend on the intrinsic Riemannian metric, volume form, and curvature tensor of the manifold or the surface. All kinematic constants of motion that arise from the resulting kinematic conservation laws also will be determined. These results generalize earlier work on finding all kinematic local conservation laws on moving domains for inviscid compressible fluid flow in n-dimensional Euclidean space.
Stephen Anco is a full professor in the Department of Mathematics & Statistics at Brock University, Canada. He is a co-author of two books in the Springer Applied Mathematics Series and has published over 60 papers. His research encompasses several areas of mathematical physics, including classical gauge field theory, General Relativity, symmetries and conservation laws of differential equations, integrable systems, and geometric curve flows. At Brock, he has served as Department Chair from 2009 to 2012 and Graduate Program Director from 2005 to 2007.