Generalized stochastic flows and applications to incompressible viscous fluids
Language
en
Article de revue
This item was published in
Bulletin des Sciences Mathématiques. 2014-06-02, vol. 138, n° 4, p. 565-584
Elsevier
English Abstract
We introduce a notion of generalized stochastic flows on manifolds, that extends to the viscous case the one defined by Brenier for perfect fluids. Their kinetic energy extends the classical kinetic energy to Brownian ...Read more >
We introduce a notion of generalized stochastic flows on manifolds, that extends to the viscous case the one defined by Brenier for perfect fluids. Their kinetic energy extends the classical kinetic energy to Brownian flows, defined as the $L^2$ norm of their drift. We prove that there exists a generalized flow which realizes the infimum of the kinetic energy among all generalized flows with prescribed initial and final configuration. We also construct generalized flows with prescribed drift and kinetic energy smaller than the $L^2$ norm of the drift. The results are actually presented for general $L^q$ norms, thus including not only the Navier-Stokes equations but also other equations such as the porous media.Read less <
ANR Project
/ - ANR-09-BLAN-0364
Origin
Hal imported