论文标题
与恒定碰撞内核的Boltzmann方程的良好/不良分叉
Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
论文作者
论文摘要
我们考虑使用恒定碰撞内核的3D玻尔兹曼方程。我们使用非线性色散PDE的方法研究了良好/不良的问题。我们构建了一个特殊解决方案的家庭，既不是平衡也不相似的方程式，并证明了$ h^{s} $ sobolev Space中的良好/不稳定性阈值恰好是规律性$ s = 1 $，尽管该公式是$ s = \ frac s = \ frac varriant in cable bunvariant。
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 $s=\frac{1}{2}$.
