检索结果-南通市图书馆

Acta Mathematica Scientia 2024年第1期44卷 195-214页

作者：丁时进李颖花王喻 School of Mathematical Sciences South China Normal UniversityGuangzhou510631China

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase *** consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/***,we obtain the global C^(∞)-solutions if the initial data is smooth.

关键词： Navier-Stokes/Allen-Cahn system density-dependent viscosity free boundary global solutions

Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity

在线全文

学校读者我要写书评

暂无评论

Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第10期8卷 1681-1690页

作者： ZHANG Ting FANG Dao-yuan Department of Mathematics Zhejiang University Hangzhou 310027 China

We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.

关键词： Compressible Navier-Stokes equations Vacuum states density-dependent viscosity

Remarks on One-Dimensional Compressible Navier-Stokes Equations with density-dependent viscosity and Vacuum

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2010年第10期26卷 2015-2030页

作者： Zhen Hua GUO Chang Jiang ZHU Center for Nonlinear Studies and Department of Mathematics Northwest University Xi'an 710069 P. R. China Laboratory of Nonlinear Analysis Department of Mathematics Central China Normal University Wuhan 4300794 P. R. China

The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coefficient u is proportional to pθ with 0 〈 θ 〈 1, the global existence and the uniqueness of weak solutions are proved which improves the previous results in [Vong, S. W., Yang, T., Zhu, C. J.： Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum II. J. Differential Equations, 192（2）, 475-501 （2003）]. Here p is the density. Moreover, a stabilization rate estimate for the density as t → ＋∞ for any θ 〉 0 is also given.

关键词： Compressible Navier-Stokes equations density-dependent viscosity vacuum asymptotic behavior

The global classical solution to a 1D two-fluid model with density-dependent viscosity and vacuum

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2022年第12期65卷 2563-2582页

作者： Senming Chen Changjiang Zhu Department of Mathematics Shantou UniversityShantou 515063China School of Mathematics South China University of TechnologyGuangzhou 510641China

In this paper, we consider the initial-boundary problem for a 1D two-fluid model with densitydependent viscosity and vacuum. The pressure depends on two variables but the viscosity only depends on one of the densities. We prove the global existence and uniqueness of the classical solution in the one-dimensional space with large initial data and vacuum. We use a new Helmholtz free energy function and the material derivative of the velocity field to deal with the general pressure with two variables, without the equivalence condition. We also develop a new argument to handle the general viscosity.

关键词： two-fluid model density-dependent viscosity vacuum global classical solution

Global Strong Solutions of the Cauchy Problem for 1D Compressible Navier-Stokes Equations with density-dependent viscosity

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2017年第1期33卷 25-34页

作者： Sheng-quan LIU Jun-ning ZHAO School of Mathematics Liaoning University School of Mathematical Sciences Xiamen University

We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ（ρ） = Aρα, where α〉 0 and A 〉0. The global existence of strong solutions is obtained, which improves the previous results by enlarging the interval of α. Moreover, our result shows that no vacuum is developed in a finite time provided the initial data does not contain vacuum.

关键词： Navier-Stokes equations global strong solution density-dependent viscosity

GLOBAL CLASSICAL SOLUTION TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH density-dependent viscosity

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2016年第5期36卷 1419-1432页

作者：叶嵎林 School of Mathematics and Statistics Henan University Kaifeng 475004 China

In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.

关键词： global existence classical solution compressible Navier-Stokes equations density-dependent viscosity vacuum

STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH density-dependent viscosity

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2016年第1期36卷 34-48页

作者：何躏唐少君王涛 School of Mathematics and Statistics Wuhan University

We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.

关键词： viscous shock waves density-dependent viscosity one-dimensional compress-ible Navier-Stokes equations nonlinear stability large density oscillation

Vacuum states on compressible Navier-Stokes equations with general density-dependent viscosity and general pressure law

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2007年第8期50卷 1173-1185页

作者： Mei-man SUN Chang-jiang ZHU Laboratory of Nonlinear Analysis Department of MathematicsCentral China Normal UniversityWuhan 430079China

In this paper,we study the one-dimensional motion of viscous gas with a general pres- sure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a *** prove the global existence and the uniqueness of weak solutions to the compressible Navier-Stokes equations by using the line *** this,some new a priori estimates are obtained to take care of the general viscosity coefficientμ(ρ)instead ofρ~θ.

关键词： Navier-Stokes equations density-dependent viscosity vacuum global existence 35Q30 76D05 35B45

ZERO DISSIPATION LIMIT TO RAREFACTION WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SELECTED density-dependent viscosity

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2021年第5期41卷 1635-1658页

作者： Yifan SU Zhenhua GUO School of Mathematics CNSNorthwest UniversityXi'an 710127China

This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent *** particular,we focus our attention on the viscosity taking the formμ(ρ)=ρ^(ϵ)(ϵ>0).For the selected density-dependent viscosity,it is proved that the solutions of the one-dimensional compressible Navier-Stokes equations with centered rarefaction wave initial data exist for all time,and converge to the centered rarefaction waves as the viscosity vanishes,uniformly away from the initial *** and subtle analysis is developed to overcome difficulties due to the selected density-dependent viscosity to derive energy estimates,in addition to the scaling argument and elementary energy ***,our results extend the studies in[Xin Z *** Pure Appl Math,1993,46(5):621-665].

关键词： compressible Navier-Stokes equations density-dependent viscosity rarefaction wave zero dissipation limit

COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH density-dependent viscosity

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2006年第2期21卷 165-178页

作者：张挺 Dept. of Math. Zhejiang Univ. Hangzhou 310027China

The global existence of solutions to the equations of one-dimensional compressible flow with density-dependent viscosity is proved. Specifically,the assumptions on initial data are that the modulo constant is stated at x=∞ ＋and x=-∞ ,which may be different ,the density and velocity are in L^z ,and the density is bounded above and below away from zero. The results also show that even under these conditions, neither vacuum states nor concentration states can be formed in finite time.

关键词： Navier-Stokes equation density-dependent viscosity global existence.