具有恒定碰撞内核的玻尔兹曼方程的良好/全拟合分岔

IF 2.4 1区数学 Q1 MATHEMATICS Annals of Pde Pub Date : 2024-07-24 DOI:10.1007/s40818-024-00177-w

Xuwen Chen, Justin Holmer

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引用次数: 0

摘要

我们考虑了具有恒定碰撞核的三维玻尔兹曼方程。我们使用非线性分散 PDEs 的方法研究了好/坏摆性问题。我们为该方程构建了一个既不接近平衡也不自相似的特殊解族，并证明尽管该方程在 \( s=\frac{1}{2}\) 时是尺度不变的，但在\(H^{s}\) Sobolev空间中的井/ill-posedness阈值恰好是正则性\(s=1\)。

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Well/Ill-Posedness Bifurcation for the Boltzmann Equation with Constant Collision Kernel

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 \( s=\frac{1}{2}\).

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来源期刊

Annals of Pde Mathematics-Geometry and Topology

CiteScore

3.70

自引率

3.60%

发文量