论文标题
矩传的传播和无与伦比的非固定玻尔兹曼方程的尖锐收敛速率
Propagation of moments and sharp convergence rate for inhomogeneous non-cutoff Boltzmann equation with soft potentials
论文作者
论文摘要
当初始基准靠近{\ it Global Maxwellian}时，我们证明了具有软电位的非切割Boltzmann方程的良好性，并且仅在$ l^2 $空间的大速度下具有多项式衰变。结果，我们得到了指数矩}的{\ IT繁殖}和{\ it rate速率}的{\ it速率}，{\ it Global Maxwellian}似乎是具有软电位的原始方程的第一个结果。证明的新成分在于局部技术，半群方法以及在$ l^2 $空间中多项式和指数力矩的传播。
We prove the well-posedness for the non-cutoff Boltzmann equation with soft potentials when the initial datum is close to the {\it global Maxwellian} and has only polynomial decay at the large velocities in $L^2$ space. As a result, we get the {\it propagation of the exponential moments} and the {\it sharp rates} of the convergence to the {\it global Maxwellian} which seems the first results for the original equation with soft potentials. The new ingredients of the proof lie in localized techniques, the semigroup method as well as the propagation of the polynomial and exponential moments in $L^2$ space.
