Korteweg modeled the dynamics of fluids in which there is not only dissipation of energy (which is characterized by the Navier-Stokes equations), but also dispersion, or the smearing of energy into ...

The equations work. They describe fluid flows as reliably as Newton’s equations predict the future positions of the planets; ... (known as the “energy inequality”).

“It’s simply not possible to describe fluids by the Navier-Stokes equations as people had thought.” In 1934, the mathematician Jean Leray discovered a novel class of solutions. These solutions could ...