论文标题
动力学Schauder估计具有时间的系数和唯一性的Landau方程式
Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation
论文作者
论文摘要
我们证明了Schauder估算的动力学Fokker-Planck方程，该方程仅需要Hölder的规律性和速度，但不及时。作为应用程序，我们推断出经典解决方案的弱独特性结果，从最初的数据开始，从$ x $中的Hölder规律性开始，并且仅在$ v $中具有连续性的对数模量。这取代了两个变量中需要Hölder连续性的较早结果。
We prove a Schauder estimate for kinetic Fokker-Planck equations that requires only Hölder regularity in space and velocity but not in time. As an application, we deduce a weak-strong uniqueness result of classical solutions to the spatially inhomogeneous Landau equation beginning from initial data having Hölder regularity in $x$ and only a logarithmic modulus of continuity in $v$. This replaces an earlier result requiring Hölder continuity in both variables.
