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Blow‐up of the smooth solutions to the compressible Navier–Stokes equations
Author(s) -
Wang Guangwu,
Guo Boling,
Fang Shaomei
Publication year - 2017
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.4384
Subject(s) - mathematics , compressibility , navier–stokes equations , mathematical analysis , hagen–poiseuille flow from the navier–stokes equations , space (punctuation) , boundary (topology) , slip (aerodynamics) , mechanics , computer science , thermodynamics , physics , operating system
In this paper, we will firstly extend the results about Jiu, Wang, and Xin (JDE, 2015, 259, 2981–3003). We prove that any smooth solution of compressible fluid will blow up without any restriction about the specific heat ratio γ . Then we prove the blow‐up of smooth solution of compressible Navier–Stokes equations in half space with Navier‐slip boundary. The main ideal is constructing the differential inequality. Copyright © 2017 John Wiley & Sons, Ltd.