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Analysis of a Diffuse Interface Model for Compressible Flows with van der Waals Equation of State

2018-11-01
 

Academic Report

Title: Analysis of a Diffuse Interface Model for Compressible Flows with van der Waals Equation of State

Reporter: Prof. SHI Xiaoding (Beijing University of Chemical Technology)

Time: November 10, 2018 (Saturday) AM 9:30-10:30

Location: A1101# room, Innovation Park Building

Contact: WANG Wendong (tel:84708351-8139)

 

Abstract: This talk is concerned with a diffuse interface model for the gas-liquid phase transition. The model consists the compressible Navier-Stokes equations with van der Waals equation of state and a modified Allen-Cahn equation. The global existence and the sharp interface limit of the strong solution is considered. Furthermore, the phase variable and the density of the gas-liquid mixture are proved to stay in the physical reasonable interval. The proofs are based on the elementary energy method and the method of matched asymptotic expansion, but with new development, where some techniques are introduced to establish the uniform bounds of the density and to treat the non-convexity of the pressure function.

 

The brief introduction to the reporter: Shi Xiaoding, Professor of Beijing University of Chemical Technology. He graduated from the Institute of mathematics and systems science, Chinese Academy of Sciences. His main research fields are fluid mechanics equations, some of which are published in the famous journals of mathematics, such as Comm. Math. Phys., SIAM J. Math. Anal., Indiana Univ. Math. J., Nonlinearity, J. Differential Equations, etc., and he has hosted many projects of the National Natural Science Foundation of China.