What are...the Navier-Stokes equations?

Video Description

Goal. I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much. This time. What are...the Navier-Stokes equations? Or: Fluids are difficult. Disclaimer. Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references. Slides. http://www.dtubbenhauer.com/youtube.html TeX files for the presentation. https://github.com/dtubbenhauer/My-TeX-files Thumbnail. Picture created using https://www.wolfram.com/language/12/nonlinear-finite-elements/navier-stokes-equation.html?product=mathematica Main discussion. https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness https://en.wikipedia.org/wiki/Millennium_Prize_Problems Background material. https://mathscinet.ams.org/mathscinet/relay-station?mr=0254401 https://en.wikipedia.org/wiki/Category:Differential_equations https://en.wikipedia.org/wiki/Partial_differential_equation https://en.wikipedia.org/wiki/Newtonian_fluid https://en.wikipedia.org/wiki/Conservation_of_mass https://en.wikipedia.org/wiki/Momentum https://en.wikipedia.org/wiki/Fluid_dynamics https://en.wikipedia.org/wiki/Partial_derivative https://en.wikipedia.org/wiki/Multivariable_calculus https://en.wikipedia.org/wiki/Partial_differential_equation#Analytical_solutions https://en.wikipedia.org/wiki/Partial_differential_equation#Numerical_solutions https://en.wikipedia.org/wiki/Linear_differential_equation Computer talk. https://doc.sagemath.org/html/en/reference/calculus/sage/calculus/desolvers.html https://doc.sagemath.org/html/en/prep/Quickstarts/Differential-Equations.html https://ask.sagemath.org/question/8239/solving-a-system-of-differential-equations/ Pictures used. https://en.wikipedia.org/wiki/Pendulum_%28mechanics%29#/media/File:Pendulum_gravity.svg https://cdn.britannica.com/22/2522-004-E94C5246/sphere-vortices-velocity-flow-B.jpg Picture from https://www.youtube.com/watch?v=CMYISqxS3K4&t=72s https://miro.medium.com/v2/resize:fit:1400/1*iQqBkmIXfkScFwYtZrgwxg.png https://secretofflight.files.wordpress.com/2012/03/volvocar.jpg https://www.comsol.com/multiphysics/navier-stokes-equations https://ins.uni-bonn.de/media/public/u/griebel/AWFD/UsersGuide/AWFD/om19.gif YouTube and co. https://www.youtube.com/watch?v=CMYISqxS3K4&t=72s https://www.youtube.com/watch?v=ERBVFcutl3M https://www.youtube.com/watch?v=zWdnf3Uh1RE https://www.youtube.com/watch?v=Ra7aQlenTb8 https://www.youtube.com/watch?v=8wXWEsHR47A #analysis #fluidmechanics #mathematics