[01532] Recent Trends in Fluid Mechanics and its Applications
Session Time & Room : 1C (Aug.21, 13:20-15:00) @G704
Type : Proposal of Minisymposium
Abstract : The aim of this minisymposium is to bring together mathematicians to share their recent progress and to inspire new ideas in applied mathematics.
This minisymposium may address modeling various phenomenum arising from gas dynamics, astrophysics, engineering, and material science, as well as theoretic analysis in problems of kinetic theory, planetary atmospheric science, traffic flow, and semiconductor etc.
[01972] Global BV solution and relaxation limit for Greenberg-Klar-Rascle model
Format : Talk at Waseda University
Author(s) :
Ying-Chieh Lin (National University of Kaohsiung)
Shih-Wei Chou (Soochow University)
John M. Hong (National Central University)
Hsin-Yi Lee (National Cheng Kung University)
Abstract : In this talk, we consider the Greenberg-Klar-Rascle multi-lane traffic flow model. This model is a relaxation system with the equilibrium state that is a discontinuous function of the car density. We study the existence of global entropy solutions and the relaxation limit for the GKR model. To construct the approximate solutions, we find two sequences of invariant regions under some suitable condition of initial data. As the relaxation time approaches 0, we prove that the limit of the entropy solutions for the GKR model is a weak solution of its equilibrium equation. It is interesting that the equilibrium equation is a scalar conservation law with discontinuous flux.
[02450] Global Transonic Solutions of Compressible Euler-Poisson Equations in Semiconductors
Format : Talk at Waseda University
Author(s) :
Shih-Wei Chou (Soochow University)
Chia-Chieh Jay Chu (National Tsing Hua University)
John M Hong (National Central University)
Abstract : In this talk, we consider an initial-boundary value problem of compressible Euler-Poisson equations arising in semiconductors. The equations form a 3-by-3 hyperbolic system of balnace laws with the global source. We establish the global existence of the transonic entropy solution by framework of a generized Glimm scheme. This is a joint work with John Hong and Jay Chu.
[02456] Finite Speed of Propagation of the Relativistic Landau and Boltzmann Equations
Format : Talk at Waseda University
Author(s) :
Ming Jiea Lyu (Chung Yuan Christian University)
Kung Chien Wu (National Cheng Kung University,)
Baoyan Sun (Yantai University)
Abstract : In this talk, we will study the relativistic Boltzmann and Landau equations in the whole space ${\mathbb{R}}^{3}$ under the closed to equilibrium setting. We recognize the finite speed of propagation of the solution in $L^{\infty}_{v,p}L^{\infty}_{x}$ and $L^{2}_{v}L^{\infty}_{x}$.
[02865] Global Transonic Solutions of Hot-Jupiter Model for exoplanetary atmosphere
Format : Talk at Waseda University
Author(s) :
Po-Chih Huang (Natonal Chung Cheng University)
Abstract : The hydrodynamic escape problem (HEP) for Hot Jupiter model, which is characterized by a inital-boundary value problem of Euler equation with exoplanetary gravity, heat, and tidal force cuased by star, is crucial for investigating the evolution of planetary atmospheres. In this paper, the global existence of transonic solutions to the HEP is established using the generalized Glimm method. The new version of Riemann and boundary-Riemann solvers, are provided as building blocks of the generalized Glimm method by inventing the contraction matrices for the homogeneous Riemann or boundary-Riemann solutions. The extended Glimm-Goodman wave interaction estimates are investigated for obtaining a stable scheme and the lower bound of the gas velocity, which matches the physical observation. The limit of approximation solutions serves as an entropy solution of bounded variations. Moreover, the range of the feasible hydrodynamical region is also obtained.
