论文标题
凸域固定玻尔兹曼方程的规律性
Regularity of Stationary Boltzmann equation in Convex Domains
论文作者
论文摘要
对于有限域中的Boltzmann方程来说，较高的规律性估计是一个充满挑战的问题。确实，即使对于诸如磁盘或球体等对称的凸形域，也众所周知，即使在[15]中，在[15]中具有“在边界处的二阶导数不存在”。在本文中，我们通过将$ c^{1，β} $解决方案构造出远离放牧边界的$ c^{1，β} $解决方案的任何$β<1 $的解决方案，以固定的boltzmann方程，并在严格的孔隙率域中，只要光滑的壁温度很小，就可以在严格的convex域中使用非等体性分散边界条件。
Higher regularity estimate has been a challenging question for the Boltzmann equation in bounded domains. Indeed, it is well-known to have "the non-existence of a second order derivative at the boundary" in [15] even for symmetric convex domains such as a disk or sphere. In this paper we answer this question in the affirmative by constructing the $C^{1,β}$ solutions away from the grazing boundary, for any $β<1$, to the stationary Boltzmann equation with the non-isothermal diffuse boundary condition in strictly convex domains, as long as a smooth wall temperature has small fluctuation pointwisely.
