论文标题
瞬时平滑和溶液的指数衰减，用于变性演化方程，并应用于玻尔兹曼方程
Instantaneous smoothing and exponential decay of solutions for a degenerate evolution equation with application to Boltzmann's equation
论文作者
论文摘要
我们建立了一种瞬时平滑属性，用于在某些退化的希尔伯特空间值进化方程的半行$（0，+\ infty）$上腐烂的溶液，包括在动力学理论中，特别是稳定的玻尔兹曼方程。我们的结果回答了Pogan和Pogan和Zumbrun在处理此类方程式的$ H^1 $稳定流动过程中提出的两个主要开放问题，表明$ l^2_ {loc} $ solutions在$ l^\ infty $（i）衰减中仍然足够小，$ c^\ iffty $ c^\ for $ c^\ iffty $ t Lies $ c^\ t> $ t LIST $ c^\ t> $ t LIST $ t> 0 liest $ t> 0 Pogan和Zumbrun
We establish an instantaneous smoothing property for decaying solutions on the half-line $(0,+\infty)$ of certain degenerate Hilbert space-valued evolution equations arising in kinetic theory, including in particular the steady Boltzmann equation. Our results answer the two main open problems posed by Pogan and Zumbrun in their treatment of $H^1$ stable manifolds of such equations, showing that $L^2_{loc}$ solutions that remain sufficiently small in $L^\infty$ (i) decay exponentially, and (ii) are $C^\infty$ for $t>0$, hence lie eventually in the $H^1$ stable manifold constructed by Pogan and Zumbrun
