论文标题
Landau方程作为梯度流
The Landau equation as a Gradient Flow
论文作者
论文摘要
我们提出了一个梯度流的透视图，以使空间均匀的兰道方程具有软电位。我们基于Landau方程的熵耗散，在概率度量的空间上构建定制度量。在此度量标准下，Landau方程可以被描述为玻尔兹曼熵的梯度流。特别是，我们通过功能不平等表征了PDE的动力学，该功能不平等通常被称为耗能不等式。此外，类似于最佳运输设置，我们表明该解释可以在最小化运动方案中使用，以构建正规兰道方程的解决方案。
We propose a gradient flow perspective to the spatially homogeneous Landau equation for soft potentials. We construct a tailored metric on the space of probability measures based on the entropy dissipation of the Landau equation. Under this metric, the Landau equation can be characterized as the gradient flow of the Boltzmann entropy. In particular, we characterize the dynamics of the PDE through a functional inequality which is usually referred as the Energy Dissipation Inequality. Furthermore, analogous to the optimal transportation setting, we show that this interpretation can be used in a minimizing movement scheme to construct solutions to a regularized Landau equation.
