腾讯会议 ID：760-550-900

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https://meeting.tencent.com/dm/7Ob6BALn2IKv

Even though there are extensive studies on the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer for the incompressible Navier-Stokes equations, there are much less mathematical results in the compressible setting. In this talk, we will present a new approach to study the compressible Navier-Stokes equations in the subsonic and high Reynolds number regime. The key observation is to introduce two new decompositions that involve quasi-compressible and Stokes approximations. And then an iteration scheme is defined by applying the decompositions for solving the linearized compressible Navier-Stokes equations. As a by-product, an analogue of the classical Orr-Sommerfeld equation is derived in the compressible setting.

With the above analytic tools, we show the spectral instability of subsonic boundary layer that is related to the Tollmien-Schlichting waves with critical Gevrey index 3/2 in the compressible setting that has been well investigated for the incompressible flow.

The talk will mainly focus on some recent joint work with Zhu Zhang.