Visualizing Ricci flow of manifolds of revolution.
Rubinstein, J.Hyam, Sinclair, Robert (2005)
Experimental Mathematics
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Displaying similar documents to “ A convergence result for the Gradient Flow of ∫ |A| 2 in Riemannian Manifolds ”
Visualizing Ricci flow of manifolds of revolution.
Mathematical foundation of flow of glaciers and large ice masses
Kolumban Hutter (1985)
Banach Center Publications
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On MHD fluctuating flow in slip-flow regime with variable suction
V. M. Soundalgekar (1971)
Matematički Vesnik
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Nonexistence of Coherent Structures in Two-dimensional Inviscid Channel Flow
H. Kalisch (2012)
Mathematical Modelling of Natural Phenomena
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Two-dimensional inviscid channel flow of an incompressible fluid is considered. It is shown that if the flow is steady and features no horizontal stagnation, then the flow must necessarily be a parallel shear flow.
On the -instability of fluid flows
Alexander Shnirelman (1999-2000)
Séminaire Équations aux dérivées partielles
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Unsteady stratified flow past a cylinder
D. V. Krishna (1966)
Applicationes Mathematicae
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On the -instability and -controllability of steady flows of an ideal incompressible fluid
Alexander Shnirelman (1999)
Journées équations aux dérivées partielles
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In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady...
Anisotropic geometric functionals and gradient flows
Giovanni Bellettini, Luca Mugnai (2009)
Banach Center Publications
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We survey some recent results on the gradient flow of an anisotropic surface energy, the integrand of which is one-homogeneous in the normal vector. We discuss the reasons for assuming convexity of the anisotropy, and we review some known results in the smooth, mixed and crystalline case. In particular, we recall the notion of calibrability and the related facet-breaking phenomenon. Minimal barriers as weak solutions to the gradient flow in case of nonsmooth anisotropies are proposed....
On bounded channel flows of viscoelastic fluids
Marshall J. Leitman, Epifanio G. Virga (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We show that the smooth bounded channel flows of a viscoelastic fluid exhibit the following qualitative feature: Whenever the channel is sufficiently wide, any bounded velocity field satisfying the homogeneous equation of motion is such that if the flow stops at some time, then the flow is never unidirectional throughout the channel. We first demonstrate the qualitative property of the bounded channel flows. Then we show explicitly how a piecewise linear approximation of a relaxation...
Mean curvature flow and self-similar submanifolds
Henri Anciaux (2002-2003)
Séminaire de théorie spectrale et géométrie
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The heat equation on manifolds as a gradient flow in the Wasserstein space
Matthias Erbar (2010)
Annales de l'I.H.P. Probabilités et statistiques
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We study the gradient flow for the relative entropy functional on probability measures over a riemannian manifold. To this aim we present a notion of a riemannian structure on the Wasserstein space. If the Ricci curvature is bounded below we establish existence and contractivity of the gradient flow using a discrete approximation scheme. Furthermore we show that its trajectories coincide with solutions to the heat equation.