Sequential stability of weak solutions in compressible self‐gravitating fluids and stationary problem | Zendy

Wang Weiwei | Zendy; Jiang Fei | Zendy; Gao Zhensheng | Zendy

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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.

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