### 学术报告八十四：江宁 — Grad-Caflisch type decay estimates of pseudo-inverse of linearized Boltzmann operator and application to Hilbert expansion of compressible Euler scaling（流体力学中的偏微分方程系列讲座之三 ）

###### 时间：2022-09-08作者：点击数:_showDynClicks("wbnews", 1747959454, 5705)

we prove some Grad-Caflisch type decay estimates of the pseudo-inverse of linearized Boltzmann collision operator,including both the hard potential ($0 \leq \gamma \leq 1$) and part of soft ($- \frac{3}{2} < \gamma < 0$) potential cutoff interaction kernels. The key idea is that the weighted $L^\infty$-norms of $( \L - \nu ) f$ are first dominated by the weighted $L^2$-norms of $f$, and then the $L^2$-norms are bounded by the $L^\infty$-norms of $\L f$ via the hypocoercivity of the weighted operator $\L$. The proof of the weighted hypocoercivity employs the high-low velocities estimates argument. Finally, these decay estimates are further applied to derive some new point-wise estimates for the Hilbert expansion terms of the Boltzmann equation in the compressible Euler scaling.