Generalized stochastic flows and applications to incompressible viscous fluids
Idioma
en
Article de revue
Este ítem está publicado en
Bulletin des Sciences Mathématiques. 2014-06-02, vol. 138, n° 4, p. 565-584
Elsevier
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Proyecto ANR
/ - ANR-09-BLAN-0364
Orígen
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