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Sequential stability of weak solutions in compressible self‐gravitating fluids and stationary problem
Author(s) -
Wang Weiwei,
Jiang Fei,
Gao Zhensheng
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1613
Subject(s) - bounded function , domain (mathematical analysis) , mathematics , constant (computer programming) , adiabatic process , stationary solution , compressibility , stability (learning theory) , compressible flow , mathematical analysis , physics , thermodynamics , computer science , machine learning , programming language
In this paper, we prove the sequential stability of weak solutions over time, in relation to the Navier–Stokes system of compressible self‐gravitating fluids in a three‐dimensional domain. As a byproduct, we show that there exists at least one non‐negative solution to the stationary problem in any bounded domain with a given mass for the adiabatic constant γ > 3 ∕ 2. In particular, for the spherically symmetric case, these conclusions still hold for γ > 4 ∕ 3 or γ = 4 ∕ 3 with a small mass. Copyright © 2012 John Wiley & Sons, Ltd.