By Caterina Calgaro, Jean-François Coulombel, Thierry Goudon
This quantity collects the contributions of a convention held in June 2005 on the laboratoire Paul Painleve (UMR CNRS 8524) in Lille, France. The assembly used to be meant to study scorching themes and destiny traits in fluid dynamics, with the target to foster exchanges of assorted viewpoints (e.g. theoretical, and numerical) at the addressed questions. It contains a suite of analysis articles on contemporary advances within the research and simulation of fluid dynamics.
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Extra info for Analysis and Simulation of Fluid Dynamics (Advances in Mathematical Fluid Mechanics)
Hence, the ith component of the regularization term (6) is nothing but the associated entropy rate of production. At the present stage, we do not assume convexity in the mapping v → ui (v) nor suppose that each of the possible (second order) nonconservative products in (6) keeps a constant sign (say negative). Rephrasing the above observations in (6)–(8), the existence of the change of variable v → u(v) in (5) thus requires the existence of as many additional entropy pairs with independent gradients for (3) than there exist scalar equations involving genuine nonconservative products in (3).
44] L. Sundbye. Existence for the Cauchy Problem for the Viscous Shallow Water Equations. Rocky Mountain Journal of Mathematics, 1998, 28 (3), 1135–1152.  L. Sundbye. Global existence for Dirichlet problem for the viscous shallow water equations. J. Math. Anal. Appl. 202 (1996), 236–258. -P. Vila. Shallow water equations for laminar ﬂows of newtonian ﬂuids. Paper in preparation and private communication, (2005).  W. -J. Xu. The Cauchy problem for viscous shallow water equations Rev. Mat.
238, 1-2, (2003), pp. 211–223.  D. Bresch, M. K. Lin. An example of low Mach (Froude) number eﬀects for compressible ﬂows with nonconstant density (height) limit. M2AN, Vol. 39, N◦ 3, pp. 477–486, (2005).  D. Bresch, A. -L. P. Xin. Eﬀective viscosity and dispersion (capillarity) approximations to hydrodynamics. Forthcoming paper, (2005).  D. Bresch, G. M´ etivier. Global existence and uniqueness for the lake equations with vanishing topography: elliptic estimates for degenerate equations.