| Abstract: |
| The Landau equation is an integro-differential kinetic model that describes the evolution of a particle density in phase space, in a regime where grazing collisions predominate. This talk will focus on recent results that provide sufficient conditions for weak solutions to be $C^\infty$ in all variables. First, by iteratively applying local regularity estimates, we show that solutions are smooth as long as the mass, energy, and entropy are bounded above, and the mass is bounded away from zero. Next, using a probabilistic argument, we show that the mass is always bounded below by a positive quantity, so this lower bound can be removed as a hypothesis. We will also briefly discuss the implications of these results for the existence theory of the Landau equation. |
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