Global classical solutions to the 3D Navier–Stokes–Korteweg equations with small initial energy
2017 ◽
Vol 16
(01)
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pp. 55-84
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Keyword(s):
In this paper, we investigate the global well-posedness of classical solutions to three-dimensional Cauchy problem of the compressible Navier–Stokes type system with a Korteweg stress tensor under the condition that the initial energy is small. This result improves previous results obtained by Hattori–Li in [H. Hattori and D. Li, Solutions for two dimensional system for materials of Korteweg type, SIAM J. Math. Anal. 25 (1994) 85–98; H. Hattori and D. Li. Global solutions of a high-dimensional system for Korteweg materials. J. Math. Anal. Appl. 198 (1996) 84–97.], where the existence of the classical solution is established for initial data close to an equilibrium in some Sobolev space [Formula: see text].
2011 ◽
Vol 65
(4)
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pp. 549-585
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Keyword(s):
2012 ◽
Vol 32
(6)
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pp. 2141-2160
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2005 ◽
Vol 03
(02)
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pp. 157-193
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2013 ◽
Vol 10
(03)
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pp. 537-562
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2019 ◽
Vol 47
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pp. 306-323
Keyword(s):
2016 ◽
Vol 261
(12)
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pp. 6883-6914
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2018 ◽
Vol 461
(2)
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pp. 1748-1770
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