The Ill-Posedness of the Cauchy Problem for Laplace's Equation This video explores why Laplace's equation requires a different approach compared to wave or heat equations. We analyze the stability of solutions as a parameter alpha approaches zero and demonstrate why stationary states depend on boundary conditions rather than initial data. #laplace #equation #pde #physics #cauchy

Understanding the 2D Vorticity & Mixing Equations This video visualizes a mathematical model of 2D incompressible viscous flow using the stream function and vorticity formulation. Vorticity Transport Equation: Governs the evolution of the vorticity field (ω). It accounts for the local rate of change, viscous diffusion controlled by the viscosity parameter (ν), and advective transport by the velocity field. Poisson’s Equation: Establishes the kinematic link between vorticity and the stream function (ψ). It allows the recovery of streamline structures from the distribution of vortex centers. Passive Scalar Field (S): Describes the transport and mixing of substances (like impurities or temperature) through the balance of molecular diffusion (D) and convective transport. #vorticity #fluiddynamics #engineering #numericalsimulation #turbulence

They rejected my application to Hogwarts but I still found a way to be a wizard. 🧹#illusion #magic #harrypotter

Jailbreak - Clue 5

Kiwi Eating 🥝 ASMR Your new daily ASMR habit starts here…Follow to keep it going! #asmr #satisfyingvideos #aiasmr #eating #kiwi