Abstract:We study the well/ill-posedness of the Boltzmann equation with dispersive methods. We take the constant collision kernel case as the first example. We construct a family of special solutions, which are neither near equilibrium nor self-similar, and prove the ill-posedness in Hs Sobolev space for s<1, despite the fact that the equation is scale invariant at s=1/2. Combining with the previous Chen-Denlinger-Pavlovic result regarding well-posedness, we have thus found the exact well/ill-posedness threshold.
ZOOM Information
Link: https://rochester.zoom.us/j/97108634994?pwd=RWRaczhaMVBLbWxMam8wWmIvSUpIdz09
ID: 971 0863 4994
Password: 221214
