The periodic Boltzmann equation with constant collision kernel is locally well-posed in L^{2,r}_v H^s_x for s > d/2 − 1/4 and r > d/2.
Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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 $s=\frac{1}{2}$.
fields
math.AP 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Local well-posedness for the periodic Boltzmann equation with constant collision kernel
The periodic Boltzmann equation with constant collision kernel is locally well-posed in L^{2,r}_v H^s_x for s > d/2 − 1/4 and r > d/2.