Workshop on Hydrodynamic Stability
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时间:6.12
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地点：理科一号楼425
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8: 30-8: 45
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开幕式
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主持
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章志飞（英国威廉希尔公司）
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8：45-9：15
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桂贵龙（西北大学）
Global stability of the compressible viscous surface waves in an infinite layer
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主持
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孙永忠（南京大学）
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9：15-9：45
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刘豫宁（上海纽约大学）
Sharp interface limits of some diffusive interface models
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9：45-10：15
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茶歇
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主持
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王梦（浙江大学）
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10：15-10：45
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朱昊（南京大学）
Traveling waves near a shear flow with Coriolis force
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主持
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费明稳（安徽师范大学）
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10：45-11：15
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张鑫（同济大学）
The decay property of the multidimensional compressible flow with free surface
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主持
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吕勇（南京大学）
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11：15-11：45
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王越（首都师范大学）
Some results on the well-posedness of the Prandtl Equations
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11：45-14：00
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午餐
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14：00-17：00
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自由讨论
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报告信息
(以下按照报告顺序排列)
Title: Global stability of the compressible viscous surface waves in an infinite layer
Speaker： Guilong Gui (NWU)
Abstract: In this talk, we investigate the global stability of the compressible viscous surface waves in the absence of surface tension effect with a steady-state violating Rayleigh-Taylor instability and with the reference domain being the horizontal infinite layer. The fluid dynamics are governed by the 3-D gravity-driven isentropic compressible Navier-Stokes equations. We develop a mathematical approach to establish global well-posedness of the multi-dimensional compressible Navier-Stokes system based on the Lagrangian framework, which requires no nonlinear compatibility conditions on the initial data. This is a jiont work with Prof. Zhifei Zhang.
Title: Sharp interface limits of some diffusive interface models
Speaker: Yuning Liu (NYU, Shanghai)
Abstract: The diffusive interface models are widely adopted in the description of the evolution of interfaces in continuum mechanics. These models either originate from continuum models or can be constructed to purposely reproduce a given sharp interface model when the thickness of their diffused interface trends to zero. In this talk we shall review a few classical methods in the proof of the convergence of the dynamical Ginzburg-Landau equation, a typical diffusive interface model. Then we discuss the possible applications of these methods to more sophisticated models.
Title: Traveling waves near a shear flow with Coriolis force
Speaker： Hao Zhu (NJU)
Abstract: The earth's rotation influences dynamics of large scale flows significantly. In this talk, we will discuss the number of traveling wave families near a shear flow under the influence of Coriolis force, which indicates richer long time dynamics around the shear flow than the non-rotating case. Here the traveling speeds of the traveling waves lie outside the range of the flow.
Title：The decay property of the multidimensional compressible flow with free surface
Speaker：Xin Zhang (Tongji University)
Abstract: In this talk, we discuss about the problem concerning the motion of the barotropic compressible Navier-Stokes equations in the smooth exterior domain with some free surface. By applying the method of the partial Lagrangian coordinates, the nonlinear problem reduces to the study of the Lame system with the free boundary condition. Then the classical theory of the Lp-Lq decay estimate is established for such linearized system, by taking advantage of the local energy approach. This is a joint work with Yoshihiro Shibata from Waseda University.
Title：Some results on the well-posedness of the Prandtl Equations
Speaker：Yue Wang (CNU)
Abstract: In this talk, I will first review some related results of Prandtl equations and then report our work on the gradient estimates for 2-D unsteady Prandtl Equations which also leads to a blow-up criterion. This is a joint work with Zhifei Zhang.
