Yann Brenier. Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations. Comm. Pure Appl. Math., 52(4):411--452, 1999. Home/Search Document Details and Download
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Research Directions in Mather's Theory - Gomes (Correct)
....in metereology, and shape optimization see the survey paper [Eva99] for details. Some of the main research topics in these area are (1) General linear programming problems in infinite dimension and abstract results. 2) Applications to specific models such as fluid dynamics [BBG02] BB00] [Bre99]. Partial Differential Equations and Numerical Methods By replacing the constraint that the measure is a generalized curve by vD x #(x) ###(x)d, which corresponds to a generalized di#usion, the dual problem is now related to a second order Hamilton Jacobi equation [Gom02c] ##u H(D x ....
Yann Brenier. Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations. Comm. Pure Appl. Math., 52(4):411--452, 1999.
Aubry-Mather Theory For Multi-Dimensional Maps - Gomes (2002) (Correct)
....behavior 16 7. Convergence in the continuous limit 17 References 20 1. Introduction In recent years, Monge Kantorowich optimal transport problems have been studied extensively, see for instance the review paper [Eva99] and its references. In fact, its connections with partial di#erential equation [Bre99], BB99] EG99] are extremely deep and well known. However, the connection with dynamical systems was realized only recently, and we believe that it will provided useful insights. The main goal of this paper is to explore such connections, in particular in the light of AubryMather theory ....
Yann Brenier. Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations. Comm. Pure Appl. Math., 52(4):411--452, 1999.
An Optimal Control Formulation For Inviscid Incompressible.. - Bloch, Crouch (Correct)
.... is to carry this out in material representation, where one needs a nonlinear Hodge decomposition, similar to the Moser decomposition (a diffeomorphism group analogue of the polar decomposition) discussed in Ebin and Marsden [1970] Many of these issues are addressed in work of Brenier# see, eg, Brenier [1999]. Acknowledgement: Wewould like to thank Peter Smereka for useful conversations. 6 ....
Brenier, Y. [1999] Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations. Comm. Pure Appl. Math.
The Geometry of Dissipative Evolution Equations: The Porous Medium .. - Otto (38 citations) (Correct)
....of Arnold s group of volume preserving diffeomorphisms [2] The geometry of this group is of interest, since the geodesic equation is the Lagrangian formulation of the Euler equations for an incompressible, inviscid fluid. The geometry and its pathologies is well studied, see [14] 34] 3] and [6]. Let us make more precise what we mean when we say that their geometry is orthogonal to ours. To this purpose, we replace IR N by the N dimensional torus T N and let ae 0 be the uniform density on T N . Then Pi Gamma1 (fae 0 g) is the 36 space of volume preserving transformations. ....
Y. Brenier, Minimal geodesics on groups of volume--preserving maps and generalized solutions of the Euler equations, Comm. Pure and Applied Math. (199?).
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