论文标题
全球轻度溶液用多项式尾巴用于整个空间中的玻尔兹曼方程
Global mild solution with polynomial tail for the Boltzmann equation in the whole space
论文作者
论文摘要
我们关注整个空间中玻尔兹曼方程上的凯奇问题。目的是在麦克斯威尔人附近构建全球界限的温和解决方案，而扰动承认大速度的多项式尾巴。该证明是基于Caflisch的分解，以及由Guo开发的$ L^2- l^\ Infty $相互作用技术。可以涵盖毕业生临界假设下的硬性和软潜力的全部范围。在整个空间的情况下，要克服的主要困难是解决方案的多项式时间衰减，与圆环相比，它比指数速率要慢得多。
We are concerned with the Cauchy problem on the Boltzmann equation in the whole space. The goal is to construct global-in-time bounded mild solutions near Maxwellians with the perturbation admitting a polynomial tail in large velocities. The proof is based on the Caflisch's decomposition together with the $L^2- L^\infty$ interplay technique developed by Guo. The full range of both hard and soft potentials under the Grad's cutoff assumption can be covered. The main difficulty to be overcome in case of the whole space is the polynomial time decay of solutions which is much slower than the exponential rate in contrast with the torus case.
