论文标题
平均引理的换向器方法
Commutator Method for Averaging Lemmas
论文作者
论文摘要
我们介绍了一种带有乘数的换向器，以证明平均引理，这是动力学方程溶液速度平均值的正则效应。该方法仅在傅立叶分析中仅需要基本技术，并显示了一个新的假设范围，足以使速度平均值在$ l^2（[0，t]，h^{1/2} _x）中。$，此结果不仅显示了平均置换方案的平均范围和定期范围的平均范围，还可以显示出一个有趣的连接，并提供定期效果的范围，以实现量级的范围，以实现定期效果，并列出定期效果，以确定范围的平稳效果。维度一。
We introduce a commutator method with multipliers to prove averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations. This method requires only elementary techniques in Fourier analysis and shows a new range of assumptions that are sufficient for the velocity average to be in $L^2([0,T],H^{1/2}_x).$ This result not only shows an interesting connection between averaging lemmas and local smoothing property of dispersive equations, but also provide a direct proof for the regularizing effect for the measure-valued solutions of scalar conservation laws in space dimension one.
