勷勤数学•专家报告

题      目： Nonlinear stability threshold for compressible Couette flow

报  告  人：许灵达  博士  (邀请人：林植林)

                                  香港理工大学

时      间：9月18日  10：30-11：30

地     点：数学科学学院西楼111报告厅

报告人简介:

       许灵达博士目前在香港理工大学从事博士后研究，主要研究兴趣为流体力学和动理学方程组的相关问题，主要论文发表在 Math. Ann, Adv. Math 等知名期刊。

摘      要：

       In this talk, we will introduce the result of nonlinear stablity threshold for compressible Couette flow, highlighting several key innovations. First, we introduce a new quantity that significantly weakens the lift-up effect, which is the key difficulty in shear flow problems. Second, we utilize the properties of acoustic waves to achieve crucial cancellations, a method that fundamentally differs from the incompressible case. Third, we propose a new set of decoupled diffusion waves, improving the decay of errors. This approach contrasts with previous constructions of coupled diffusion waves and can be extended to more general hyperbolic-parabolic coupled systems. Additionally, we employ a Poincaré-type inequality, aided by Huang-Li-Matsumura’s inequality, which plays an important role in managing certain critical (for time) energy estimates.

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