The lifespan of spherically symmetric solutions of the compressible Euler equations outside an impermeable sphere
The nonlinear future stability of the FLRW family of solutions to the irrotational Euler-Einstein system with a positive cosmological constant
In this article, we study small perturbations of the family of Friedmann-Lemaître-Robertson-Walker cosmological background solutions to the coupled Euler-Einstein system with a positive cosmological constant in spacetime dimensions. The background solutions model an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing exponentially accelerated expansion. Our nonlinear analysis shows that under the equation of state , the background metric + fluid solutions...
The vortex method for 2D ideal flows in the exterior of a disk
The vortex method is a common numerical and theoretical approach used to implement the motion of an ideal flow, in which the vorticity is approximated by a sum of point vortices, so that the Euler equations read as a system of ordinary differential equations. Such a method is well justified in the full plane, thanks to the explicit representation formulas of Biot and Savart. In an exterior domain, we also replace the impermeable boundary by a collection of point vortices generating the circulation...
Two dimensional incompressible ideal flow around a thin obstacle tending to a curve