论文标题
具有库仑潜力及其应用的空间均匀兰道方程的新单调公式
A new monotonicity formula for the spatially homogeneous Landau equation with Coulomb potential and its applications
论文作者
论文摘要
我们描述了一个涉及相对熵和$ \ dot {h}^1 $ seminorm的时间依赖性功能，该功能沿溶液降低，沿空间均匀的Landau方程，具有库仑电势。该单调功能的研究阐明了该方程式的耗散与非线性之间的竞争。它使有关库仑潜力的Landau方程的规律性/爆炸问题获得了新的结果。
We describe a time-dependent functional involving the relative entropy and the $\dot{H}^1$ seminorm, which decreases along solutions to the spatially homogeneous Landau equation with Coulomb potential. The study of this monotone functionial sheds light on the competition between the dissipation and the nonlinearity for this equation. It enables to obtain new results concerning regularity/blowup issues for the Landau equation with Coulomb potential.
