Analytical solutions to the 3-D compressible Navier-Stokes equations with free boundaries

被引:3
作者
Wang, Mei [1 ]
Li, Zilai [2 ]
Li, Wei [1 ]
机构
[1] Northwest Univ, Sch Math, Xian 710127, Peoples R China
[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Henan, Peoples R China
来源
BOUNDARY VALUE PROBLEMS | 2015年
基金
中国国家自然科学基金; 高等学校博士学科点专项科研基金;
关键词
analytical solution; compressible Navier-Stokes equations; density-dependent; DENSITY-DEPENDENT VISCOSITY; GLOBAL EXISTENCE; SMOOTH SOLUTIONS; WEAK SOLUTIONS; SHALLOW-WATER; FLOWS; DERIVATION; BLOWUP;
D O I
10.1186/s13661-015-0353-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we study a class of analytical solutions to the 3-D compressible Navier-Stokes equations with density-dependent viscosity coefficients, where the shear viscosity h(rho) = mu >= 0, and the bulk viscosity g(rho) = rho(beta) (beta > 0). By constructing a class of radial symmetric and self-similar analytical solutions in RN (N >= 2) with both the continuous density condition and the stress free condition across the free boundaries separating the fluid from vacuum, we derive that the free boundary expands outward in the radial direction at an algebraic rate in time and we also have shown that such solutions exhibit interesting new information such as the formation of a vacuum at the center of the symmetry as time tends to infinity and explicit regularities, and we have large time decay estimates of the velocity field.
引用
收藏
页数:15
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