Analysis Seminar

At the macroscopic level, gas dynamics is modeled by the compressible Euler equations, which admit a broad range of finite-time singularity formation scenarios, including implosions. At the mesoscopic level, gas dynamics is described by kinetic theory, with the Boltzmann and Landau equations as two of its most fundamental models. A natural and widely open question is whether the implosion singularities seen in Euler also occur in kinetic models, or whether some feature of the kinetic description prevents their formation.

I will discuss recent work on continuation criteria for the Boltzmann and Landau equations that require less control than the corresponding macroscopic quantities. As a consequence, we obtain restrictions on when a given Euler blow-up profile could be used to construct singularities in kinetic models. In particular, for the physical parameter range of the Boltzmann and Landau equations, no known Euler singularity profile can yield such a construction; for the Landau-Coulomb model, this approach to blow-up is essentially ruled out entirely. This is joint work with Chris Henderson and Luis Silvestre.

Zoom meeting ID: Slooi