Cl
synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
equality (definitional, propositional, computational, judgemental, extensional, intensional, decidable)
isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)-category
Examples.
The partial differential equation describing viscous hydrodynamics.
Terence Tao, Searching for singularities in the Navier–Stokes equations, Nature Reviews Physics (2019) (doi:10.1038/s42254-019-0068-9, pdf)
Clay Mathematical Institute, Navier-Stokes equation
See also
Wikipedia, Navier-Stokes equation
Wikipedia, Navier-Stokes existence and smoothness
Discussion of the (relativistic) Navier-Stokes equation in view of the fluid/gravity correspondence:
Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, Andrew Strominger, From Navier-Stokes To Einstein, J. High Energ. Phys. (2012) 2012: 146 (arXiv:1101.2451)
Ashok Thillaisundaram, Aspects of fluid dynamics and the fluid/gravity correspondence, 2017 (CambridgeRepositor:1810/267097, pdf)
Last revised on October 15, 2019 at 14:05:02. See the history of this page for a list of all contributions to it.