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)
identity type, equivalence of types, definitional isomorphism
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.