Stochastic Lagrangian flows on the group of volume-preserving homeomorphisms of the spheres

DOI10.1080/17442508.2014.995659zbMath1338.58024arXiv1312.2307OpenAlexW2025947439MaRDI QIDQ2804003

De Jun Luo

Publication date: 27 April 2016

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.2307

zbMATH Keywords

Brownian motionNavier-Stokes equationrotation processgroup of volume-preserving homeomorphisms

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items

Nash embedding, shape operator and Navier-Stokes equation on a Riemannian manifold, Constantin and Iyer's representation formula for the Navier-Stokes equations on manifolds

Cites Work

• Unnamed Item
• Quasi-invariant stochastic flows of SDEs with non-smooth drifts on compact manifolds
• Heat semi-group and generalized flows on complete Riemannian manifolds
• Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability
• Transport equation and Cauchy problem for BV vector fields
• A variational principle for the Navier-Stokes equation
• Brownian motion on volume preserving diffeomorphisms group and existence of global solutions of 2D stochastic Euler equation
• Ordinary differential equations, transport theory and Sobolev spaces
• Isotropic stochastic flow of homeomorphisms on \(\mathbb R^d\) associated with the critical Sobolev exponent
• Canonical Brownian motion on the diffeomorphism group of the circle
• Modulus of continuity of the canonic Brownian motion ``on the group of diffeomorphisms of the circle
• Integration of Brownian vector fields.
• Solving stochastic differential equations on \(\text{Homeo}(S^1\))
• Navier-Stokes equation and diffusions on the group of homeomorphisms of the torus
• Generalized stochastic flows and applications to incompressible viscous fluids
• Isotropic stochastic flow of homeomorphisms on \(S^{d}\) for the critical Sobolev exponent
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• LARGE DEVIATION PRINCIPLES FOR ISOTROPIC STOCHASTIC FLOW OF HOMEOMORPHISMS ON S^d
• Estimates and regularity results for the DiPerna-Lions flow
• The canonic diffusion above the diffeomorphism group of the circle
• Flow of Homeomorphisms and Stochastic Transport Equations