论文标题
在整个空间中具有软电位的非切割玻尔兹曼方程
Non-cutoff Boltzmann equation with soft potentials in the whole space
论文作者
论文摘要
当初始数据是麦克斯韦人的小扰动而在速度中多项式衰减时，我们证明了在整个空间中具有非切割软势的玻尔兹曼方程的全局解决方案的存在和独特性。我们的方法基于所需溶液分解为两个部分：一个在速度中具有多项式衰减的部分，仅使用线性化操作员的耗散部分满足玻璃体方程；另一个带有高斯衰减的速度，用耦合项验证玻尔兹曼方程。
We prove the existence and uniqueness of global solutions to the Boltzmann equation with non-cutoff soft potentials in the whole space when the initial data is a small perturbation of a Maxwellian with polynomial decay in velocity. Our method is based in the decomposition of the desired solution into two parts: one with polynomial decay in velocity satisfying the Boltzmann equation with only a dissipative part of the linearized operator ; the other with Gaussian decay in velocity verifying the Boltzmann equation with a coupling term.
