论文标题
稳定性，适应性和规律性的硬势方程
Stability, well-posedness and regularity of the homogeneous Landau equation for hard potentials
论文作者
论文摘要
我们使用某些特定的Monge-Kantorovich成本为空间均匀的Landau方程式建立了良好的和定量的稳定性，因为仅假设初始条件是对约$ P> 2 $的有限订单$ P $的概率措施。结果，我们扩展了以前的规律性结果，并表明所有非级别测量解决方案都具有有限的初始能量，并立即允许具有有限熵的分析密度。一路上，我们证明了Landau方程即时创造了高斯时刻。我们还显示了在有限初始能量的唯一假设下存在弱溶液。
We establish the well-posedness and some quantitative stability of the spatially homogeneous Landau equation for hard potentials, using some specific Monge-Kantorovich cost, assuming only that the initial condition is a probability measure with a finite moment of order $p$ for some $p>2$. As a consequence, we extend previous regularity results and show that all non-degenerate measure-valued solutions to the Landau equation, with a finite initial energy, immediately admit analytic densities with finite entropy. Along the way, we prove that the Landau equation instantaneously creates Gaussian moments. We also show existence of weak solutions under the only assumption of finite initial energy.
