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Analytical solutions to the 1D compressible isothermal Navier-Stokes equations with density-dependent viscosity
被引:6
|作者:
Dong, Jianwei
[1
]
Zhang, Litao
[1
]
机构:
[1] Zhengzhou Univ Aeronaut, Sch Math, Zhengzhou 450015, Peoples R China
关键词:
SELF-SIMILAR SOLUTIONS;
GLOBAL EXISTENCE;
SMOOTH SOLUTIONS;
EULER EQUATIONS;
WEAK SOLUTIONS;
CAUCHY-PROBLEM;
BLOW-UP;
GAS;
COEFFICIENT;
FLOWS;
D O I:
10.1063/5.0067503
中图分类号:
O4 [物理学];
学科分类号:
0702 ;
摘要:
In this paper, we construct a class of analytical solutions to the one-dimensional compressible isothermal Navier-Stokes equations with density-dependent viscosity in the real line R. Precisely, we take the pressure p(rho) = a(1)rho and the viscosity coefficient mu(rho) = a(2)rho with a(1), a(2) > 0. We show that the system has an exact solution with the initial data satisfying rho(0)(x) = e(x) and u(0)(x) = x. The large-time asymptotic behavior of the density is exhibited according to various a(1). The analytical solutions to the compressible isothermal Euler equations and the pressureless Euler equations are obtained as by-products.
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页数:6
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