Researchers are about to move beyond several fundamental questions in partial differential equations (PDEs) and Euler’s remarkable equation for an incompressible fluid will play a central role in this. The EU-funded FLUSPEC project has set out to prove that the curvature of the interface blows up in finite time due to the appearance of kinks of controlled geometry. The project will also consider a number of questions in spectral theory about the geometry of the eigenfunctions of the Laplacian and of the curl operator, analyse the process of creation and destruction of vortex structures in the 3D Navier-Stokes and Gross-Pitaevskii equations, consider blowup problems in magnetohydrodynamics, develop global approximation theorems for dispersive equations and study the limiting measures of a sequence of solutions to the Seiberg-Witten equation.

ERC-2019-COG