论文标题
线性化Landau操作员的低纤维化和光谱估计值
Hypoelliptic and spectral estimates for the linearized Landau operator
论文作者
论文摘要
我们对粒子密度f = f = f（t，x，v）的演变表示不均匀的兰道方程感兴趣，该方程在时间t $ \ ge $ 0中表示，位置x $ \ in $ r 3的位置x $ \ in $ r 3的粒子密度和$ r 3中的速度v $ \。在本文中，我们建立了低细胞估计值，即具有硬势和麦克斯韦分子的线性兰道算子的分解的频谱和估计值。该证明是基于乘数方法，需要精细的伪分辨率计算工具。
We are interested in the inhomogeneous Landau equation which describes the evolution of a particle density f = f (t, x, v) representing at time t $\ge$ 0, the density of particles at position x $\in$ R 3 and velocity v $\in$ R 3. The study is motivated by the linearization of the Landau equation near Maxwellian distribution. In this article, we establish hypoelliptic estimates, a localization of the spectrum and estimates of the resolvent of the linear Landau operator with hard potentials and Maxwellian molecules. The proof is based on a multiplier method and requires fine pseudo-differential calculus tools.
