学术报告

【online】Grad-Caflisch type decay estimates of pseudo-inverse of linearized Boltzmann......

发布人:发布时间: 2022-09-15

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题目: Grad-Caflisch type decay estimates of pseudo-inverse of linearized Boltzmann operator and application to Hilbert expansion of compressible Euler scaling


报告人: 江宁(武汉大学)

 

时间:2022年05日19 16:00-17:00


方式: 腾讯会议  ID:249-243-437  密码:123456

 

摘要: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 $(\mathscr{L} - \nu )f$ 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 $\mathscr{L} f$ via the hypocoercivity of the weighted operator $\mathscr{L}$. 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.


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