08:30-09:30 Tuesday, 8 April 2025 Auditorium, Rectorate
Abstract
We first recall, for the Euler equations of an incompressible fluid, various descriptions and approximations, in particular a “multiphasic formulation” leading to a system of PDEswhich is (rarely) hyperbolic -and therefore well-posed- or (mostly) space-time elliptic -and therefore ill-posed-, depending on the structure of the initial conditions, in close relationship with the Kelvin-Helmholtz instability. Then, we address the incompressible porous medium equations (IPME) that can be derived, through a suitable quadratic change of time, from the Euler equations in the case of an inhomogeneous incompressible fluid subject to an external potential. Somewhat surprisingly, thanks to the multiphasic formulation, the IPME, in spite of their “gradient flow” nature, read as a well-posed pseudo-differential hyperbolic system of conservation laws, which is confirmed by numerical experiments.