Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Volume 21, Issue 8, Pages 2745-2766Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2016071
Keywords
Korteweg type; compressible Navier-Stokes equations; stability; global existence; blow-up
Categories
Funding
- China NSF [11526073]
- National Basic Research Program of China (973 Program) [2013CB834100]
- NSF of Jiangsu Province [BK20150794]
- Fundamental Research Funds for the Central Universities [2014B13914]
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In this paper, we consider compressible Navier-Stokes-Korteweg (N-S-K) equations with more general pressure laws, that is the pressure P is non-monotone. We prove the stability of weak solutions in the periodic domain Omega = T-N, when N = 2,3. Utilizing an interesting Sobolev inequality to tackle the complicated Korteweg term, we obtain the global existence of weak solutions in one dimensional case. Moreover, when the initial data is compactly supported in the whole space R, we prove the compressible N-S-K equations will blow-up in finite time.
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