Stability of Vacuum for the Landau Equation with Moderately Soft Potentials
Stability of Vacuum for the Landau Equation with Moderately Soft Potentials
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DOI：
10.1007/s40818-019-0067-2
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发表时间：
2018-07
期刊：
影响因子：
2.8
通讯作者：
J. Luk
中科院分区：
文献类型：
--
作者：
J. Luk
考虑空间非齐次朗道方程，在整个空间上具有中等软势（即具有）。我们证明了，如果初始数据在适当的范数下接近真空解，则解f在时间上保持全局正则。这是第一个关于长程相互作用的二元碰撞模型的真空稳定性结果。此外，我们证明了在近真空区的解决方案的线性输运方程的解决方案。此外，一般情况下，解决方案不接近一个旅行的全球麦克斯韦。我们的证明依赖于使用加权能量估计和加权量的最大值原理捕获的稳健衰减估计。更重要的是，我们还利用了非线性朗道方程的一个空结构，它抑制了最慢衰减的相互作用。
Consider the spatially inhomogeneous Landau equation with moderately soft potentials (i.e. with) on the whole space. We prove that if the initial dataare close to the vacuum solutionin an appropriate norm, then the solutionfremains regular globally in time. This is the first stability of vacuum result for a binary collisional model featuring a long-range interaction. Moreover, we prove that the solutions in the near-vacuum regime approach solutions to the linear transport equation as. Furthermore, in general, solutions do not approach a traveling global Maxwellian as. Our proof relies on robust decay estimates captured using weighted energy estimates and the maximum principle for weighted quantities. Importantly, we also make use of anull structurein the nonlinearity of the Landau equation which suppresses the most slowly-decaying interactions.