A Model of Radiational Gaseous Stars
Xin Liu
TL;DR
This paper develops a mathematical model for radiational gaseous stars, proving existence of stationary solutions and analyzing the behavior of density and temperature near the star's boundary.
Contribution
It introduces a new model for radiational gaseous stars and establishes existence and well-posedness results for the associated free boundary and evolutionary problems.
Findings
Existence of stationary solutions to the hydrostatic equations.
Analysis of vacuum behavior near the free boundary.
Construction of a priori estimates for solutions.
Abstract
We introduce a model concerning radiational gaseous stars and establish the existence theory of stationary solutions to the free boundary problem of hydrostatic equations describing the radiative equilibrium. We also concern the local well-posedness of the moving boundary problem of the corresponding Navier-Stokes-Fourier-Poisson system and construct a prior estimates of strong and classical solutions. Our results explore the vacuum behaviour of density and temperature near the free boundary for the equilibrium and capture such degeneracy in the evolutionary problem.
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Taxonomy
TopicsNavier-Stokes equation solutions · Nonlinear Partial Differential Equations · Gas Dynamics and Kinetic Theory