Program
Fluids interface free boundary problems
Student No.:50
Time:Mon 15:20-17:20 (except for public holidays)
Instructor:Huihui Zeng  [Tsinghua University]
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2015-9-14
Ending Date:2015-12-28

Description:

 


Fluids interface problems appear in many important physical situations such as water waves, shape of gaseous stars, and gas flows though porous media. They are modeled by free boundary problems of Euler and Navier-Stokes equations. In this course, we will cover some basic theory in these topics with emphasize on the a priori estimates which lead to the well-posedness and behaviors of solutions.

 

 


Prerequisite:

 


Basic theory of PDE and Sobolev spaces.

 

 


Reference:

 


1. D. Christodoulou and H. Lindblad, On the motion of the free surface of a liquid, Comm. Pure Appl. Math. 53 (12), 1536--1602 (2000).
2. D. Coutand, S. Shkoller, Well-posedness in smooth function spaces for themovingboundary 1-D compressible Euler equations in physical vacuum. Commun. Pure Appl. Math. 64, 328–366 (2011).
3. T. Luo, Z.Xin and H. Zeng, Well-posedness for the motion of physical vacuum of the three-dimensional compressible Euler equations with or without self-gravitation, Arch. Ration. Mech. Anal. 213 (2014), 763-831.
4. T. Luo and H. Zeng, Global existence of smooth solutions and convergence to Barenblatt solutions for the physical vacuum free boundary problem of compressible Euler equations with damping, Comm. Pure Appl. Math., oneline, DOI: 10.1002/cpa.21562.
5. T. Luo, Z.Xin and H. Zeng, On nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem, arXiv:1506.03906.