Non-selfadjoint operators in gravity: two case studies
By José Luis Jaramillo
Jumps, cusps and fractals in the solution of dispersive equations
By Beatrice Pelloni
By Zoe Wyatt
Appears in collection : Mathematical aspects of the physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints
On a background Minkowski spacetime, the Euler equations (both relativistic and not) are known to admit unstable homogeneous solutions with finite-time shock formation. Such shock formation can be suppressed on cosmological spacetimes whose spatial slices expand at an accelerated rate. However, situations with decelerated expansion, which are relevant in our early universe, are not as well understood. I will present some recent joint work in this direction, based on collaborations with David Fajman, Maciej Maliborski, Todd Oliynyk and Max Ofner.