Global classical solutions to a 3D Navier–Stokes–Korteweg equations with small initial energy
Global classical solutions to a 3D Navier–Stokes–Korteweg equations with small initial energy
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DOI：
10.1142/s0219530516500123
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发表时间：
2018
影响因子：
2.2
通讯作者：
Xiaofeng Hou;Hongyun Peng;Changjiang Zhu
中科院分区：
文献类型：
--
作者：
Xiaofeng Hou;Hongyun Peng;Changjiang Zhu
本文研究了具有Korteweg应力张量的可压缩Navier-Stokes型方程组三维Cauchy问题在初始能量较小时经典解的整体适定性.这一结果改进了Hattori-Li在[H. Hattori和D.李，二维材料系统的Korteweg型的解决方案，SIAM J数学分析。25（1994）85-98; H. Hattori和D.李Korteweg材料高维系统的整体解。J. Math. Anal. 198（1996）84-97.]，其中经典解的存在性是建立在初始数据接近平衡的一些Sobolev空间Hs。
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 stess 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 Hs.