NCTS(South)/ NCKU Math Colloquium

DATE2014-09-18 16:10-17:00


SPEAKER洪盟凱 教授(中央數學系

TITLEGlobal Solutions to Inviscid Hydrodynamic Equations Arising from Extrasolar Planetary Atmospheres

ABSTRACT In this talk, we consider the three-dimensional inviscid hydrodynamic equations without thermal conduction, which is a 3 by[1] 3 nonlinear hyperbolic system of balance laws due to the spherical symmetry in space-time. We investigate the Cauchy and the initial-boundary value problems for this model, subject to the initial and boundary datum near the sonic states. An asymptotic expansion of solution for Riemann and boundary-Riemann problems is found in the series consisting of the classical Riemann solvers and the perturbations solving the linearized system of equations around solvers. We develop a generalized Glimm method to establish the existence results. The stability of the scheme is resulted from the estimates of interaction among classical elementary waves and the perturbations. The limit of approximate solutions serves as a BV entropy solution of this problem.