学术报告
Global solutions to 3D compressible Navier-Stokes equations with degenerate viscosities, and Quantum Navier-Stokes equations-Professor Alexis F. Vasseur (Department of Mathematics, University of Texas at Austin, USA)
题目：Global solutions to 3D compressible Navier-Stokes equations with degenerate viscosities, and Quantum Navier-Stokes equations
报告人：Professor Alexis F. Vasseur (Department of Mathematics, University of Texas at Austin, USA)
摘要：
We prove the existence of global weak solutions for 2D and 3D compressible Navier-Stokes equations with degenerate viscosities. These models include the viscous shallow water equations. The method is based on the Bresch and Desjardins entropy. The main contribution is to derive the Mellet-Vasseur type inequality for the weak solutions, even if it is not verified by the first level of approximation. This provides existence of global solutions in time, for the barotropic compressible Navier-Stokes equations, in three dimensional space, with large initial data, possibly vanishing on the vacuum. This is a joint work with Cheng Yu published in Inventiones Mathematicae. We will present also a recent development of this idea to the Quantum Navier-Stokes equation. The main idea is to construct renormalized solutions in velocity. This last work is in collaboration with Ingrid Lacroix-Violet.
时间：12月15日(周四) 下午 4:00--5:00
地点：首都师范大学北一区文科楼507教室
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