Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel

Abstract

We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We construct a family of special solutions, which are neither near equilibrium nor self-similar, to the equation, and prove that the well/ill-posedness threshold in $H^s$ Sobolev space is exactly at regularity $s=1$, despite the fact that the equation is scale invariant at $s=\frac{1}{2}$.

Accepted to appear in Annals of PDE

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Cited by in corpus (1)

• Well/Ill-posedness of the Boltzmann Equation with Soft Potential