论文标题
加权Sobolev空间中非切割玻尔兹曼方程的全球存在
Global Existence of Non-cutoff Boltzmann Equation in Weighted Sobolev Space
论文作者
论文摘要
本文提出了一种新的分析方法和伪分辨率的计算方法，用于推导非切割线性化玻尔兹曼方程的正则化估计值。我们能够从加权的Sobolev space $ h（a^{ - 1/2}）h^m_x $到$ h（a^{1/2}）h^m_x $的sebolev space $ h（a^{ - 1/2}）H（a^{ - 1/2}）H（a^{ - 1/2}）H（a^{ - 1/2}）H（a^{1/2}）h^m_x $连续得出的正规化估计。借助这些属性，我们证明了在非切割玻尔兹曼方程中存在全球范围的独特解决方案，以在整个空间上具有弱规则性假设对初始数据的弱势势能。我们认为，自$ h（a^{1/2}）$以来的硬性案例可以嵌入$ l^2 $中。这项工作开发了伪差分计算，频谱分析和半群理论的应用到非切割Boltzmann方程。
This article presents a new approach of semigroup analysis and pseudo-differential calculus for deriving the regularizing estimate on non-cutoff linearized Boltzmann equation. We are able to obtain regularizing estimate of semigroup $e^{tB}$ that is continuous from weighted Sobolev space $H(a^{-1/2})H^m_x$ to $H(a^{1/2})H^m_x$ with a sharp large time decay. With these properties, we prove the existence of global-in-time unique solution to the non-cutoff Boltzmann equation for hard potential on the whole space with weak regularity assumption on initial data. We consider the hard potential case since $H(a^{1/2})$ can be embedded in $L^2$. This work develops the application of pseudo-differential calculus, spectrum analysis and semigroup theory to non-cutoff Boltzmann equation.
