论文标题
具有大振幅初始数据和镜面反射边界条件的玻尔兹曼方程
The Boltzmann equation with large-amplitude initial data and specular reflection boundary condition
论文作者
论文摘要
对于具有截止硬势的Boltzmann方程式，我们构建了独特的全球解决方案，在很长的时间内与全球麦克斯韦人构建了指数级的速率，不仅是出于镜面反射边界条件，具有有界的凸C^3域，而且对于一类巨大的振幅初始数据，其中具有适当的速度重量的大幅度初始数据，而且相对较小的速度较小，而且相对较小。证据的一个关键点是引入一个微妙的非线性迭代过程，以估算沿线化动力学的三重Duhamel迭代中的增益项。
For the Boltzmann equation with cutoff hard potentials, we construct the unique global solution converging with an exponential rate in large time to global Maxwellians not only for the specular reflection boundary condition with the bounded convex C^3 domain but also for a class of large amplitude initial data where the L^infty norm with a suitable velocity weight can be arbitrarily large but the relative entropy need to be small. A key point in the proof is to introduce a delicate nonlinear iterative process of estimating the gain term basing on the triple Duhamel iteration along the linearized dynamics.
