论文标题
真空对Landau方程的稳定性
Stability of vacuum for the Landau equation with hard potentials
论文作者
论文摘要
我们在整个空间$ \ mathbb {r}^3 $上考虑具有麦克斯韦和硬势（即带有$γ\ in [0,1）$的$γ\）的空间不均匀兰道方程。我们证明，如果初始数据$ f _ {\ text {in}} $接近真空解决方案$ f _ {\ text {vac}} = 0 $在适当的加权标准中，则及时在全球范围内存在解决方案$ f $。这项工作建立在作者早期关于具有艰苦潜力的Landau方程解决方案的本地工作的工作。我们的证明使用$ l^2 $估计并利用Luk建立的无效结构[真空对Landau方程的稳定性，具有中等软势，PDE Annals（2019）5:11]。为了能够完成我们的估计，我们必须将加权能量估计值汇编，这些估计是由作者在先前的论文中建立的[Landau方程的本地存在，具有硬势，Arxiv：1910.11866]，并实现了无效的结构，并设计了新的加权规范。
We consider the spatially inhomogeneous Landau equation with Maxwellian and hard potentials (i.e with $γ\in[0,1)$) on the whole space $\mathbb{R}^3$. We prove that if the initial data $f_{\text{in}}$ are close to the vacuum solution $f_{\text{vac}}=0$ in an appropriate weighted norm then the solution $f$ exists globally in time. This work builds up on the author's earlier work on local existence of solutions to Landau equation with hard potentials. Our proof uses $L^2$ estimates and exploits the null-structure established by Luk [Stability of vacuum for the Landau equation with moderately soft potentials, Annals of PDE (2019) 5:11]. To be able to close our estimates, we have to couple the weighted energy estimates, which were established by the author in a previous paper [Local existence for the Landau equation with hard potentials, arXiv:1910.11866], with the null-structure and devise new weighted norms that take this into account.
