Global classical solutions for 3D compressible Navier-Stokes equations with vacuum and a density-dependent viscosity coefficient

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:401

Article

Liu, Shengquan^1,2  Zhang, Jianwen²  Zhao, Junning² 

[1] Liaoning Univ, Sch Math, Shenyang 110036, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

关键词: Compressible Navier-Stokes equations;    Global classical solutions;    Density-dependent viscosity;    Vacuum;   

DOI  :  10.1016/j.jmaa.2012.12.056

来源: Elsevier

【 摘 要 】

In this paper, we prove the global existence of classical solutions to the three-dimensional (3D) compressible Navier-Stokes equations with a density-dependent viscosity coefficient (lambda = lambda(rho)) provided the initial data is of small energy. This in particular implies that the solutions may have large oscillations and contain vacuum states. As a result of the uniform estimates, the large-time behavior of the solution is also studied. The result obtained generalizes those results in Zhang (2011) [39] and Huang et al. (2012) [17] where the non-vacuum initial data and the constant viscosity coefficients are considered, respectively. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free