Differential geometry on diffeomorphism groups and Lagrangian stability of viscous flows

DOI10.1016/j.physd.2006.10.011zbMath1160.37030OpenAlexW2049691445WikidataQ115341698 ScholiaQ115341698MaRDI QIDQ870856

Yodai Watanabe

Publication date: 15 March 2007

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2006.10.011

zbMATH Keywords

differential geometrydiffeomorphism groupsviscous flowsLagrangian stability

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Applications of global differential geometry to the sciences (53C80) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Hydrodynamic stability (76E99) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65) Symmetries of infinite-dimensional dissipative dynamical systems (37L20)

Related Items

Generalized stochastic flows and applications to incompressible viscous fluids

Cites Work

• Introduction to differentiable manifolds.
• Groups of diffeomorphisms and the motion of an incompressible fluid
• A geometrical method for the stability analysis of dynamical systems
• Geodesics and curvature of a group of diffeomorphisms and motion of an ideal fluid
• An integrable shallow water equation with peaked solitons
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