学术报告

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发布人：发布时间： 2020-06-30

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2020年7月5日上午 （腾讯会议ID：527 336 497，会议密码：202075） | |

| 章志飞，北京大学 Transition threshold for the 3D Couette flow in a finite channel |

| 王春朋，吉林大学 Mixed type equations and smooth transonic flows in de Laval nozzles |

| 杜力力，四川大学 Oblique injection of incompressible ideal fluid from a slot into a free stream |

**章志飞，北京大学**

**题目：** Transition threshold for the 3D Couette flow in a finite channel

**摘要： **The plane Couette flow is linearly stable for any Reynolds number. However, it could become nonlinearly unstable and transition to turbulence for small but finite perturbations at high Reynolds number. This is so-called Sommerfeld paradox. One resolution of this paradox is to study the transition threshold problem, which is concerned with how much disturbance will lead to the instability of the flow and the dependence of disturbance on the Reynolds number. In a joint work with Qi Chen and Dongyi Wei, we showed that if the initial velocity $v_0$ satisfies $\|v_0-(y,0,0)\|_{H^2}\le c_0{Re}^{-1}$ for some $c_0>0$ independent of $Re$, then the solution of the 3D Navier-Stokes equations is global in time and does not transition away from the Couette flow in the $L^\infty$ sense, and rapidly converges to a streak solution for $t\gtrsim Re^{1/3}$ due to the mixing-enhanced dissipation effect. This result confirms the transition threshold conjecture proposed by Trefethen et al.(Science, 261(1993), 578-584) for the 3D Couette flow in a finite channel with non-slip boundary condition.

**王春朋，吉林大学**

**题目：**Mixed type equations and smooth transonic flows in de Laval nozzles

**摘要：**In this talk, we introduce recent joint works with Professor Zhouping Xin on smooth transonic flows in two dimensional de Laval nozzles, which are governed by a nonlinear elliptic-hyperbolic mixed type equation with degeneracy at the sonic state. For smooth transonic potential flows whose sonic points are all exceptional, it is shown that the existence of such a smooth transonic flow is determined by the geometry and the height of the nozzle at the throat.

**杜力力，四川大学**

**题目：**Oblique injection of incompressible ideal fluid from a slot into a free stream

**摘要：**In this talk, we will discuss a two-phase fluid free boundary problem in a slot-film cooling. We will give two well-posedness results on the existence and uniqueness of the incompressible inviscid two-phase fluid with a jump relation on free interface. The problem formulates the oblique injection of an incompressible ideal fluid from a slot into a free stream. From the mathematical point of view, this work is motivated by the pioneer work in1986 by A. Friedman, in which some well-posedness results are obtained in some special case. Furthermore, A. Friedman proposed an open problem on the existence and uniqueness of the injection flow problem for more general case. The main results in this talk solve the open problem and establish the well-posedness results on the physical problem.

**邀请人：** 吕勇 老师