共查询到20条相似文献,搜索用时 31 毫秒
1.
Qin Duan 《Journal of Differential Equations》2011,250(6):2687-2714
In this paper, we study a free boundary problem of one-dimensional compressible Navier-Stokes equations with a density-dependent viscosity, which include, in particular, a shallow water model. Under some suitable assumptions on the initial data, we obtain the global existence, uniqueness and the large time behavior of weak solutions. In particular, it is shown that a stationary wave pattern connecting a gas to the vacuum continuously is asymptotically stable for small initial general perturbations. 相似文献
2.
S. V. Khabirov 《Journal of Applied Mathematics and Mechanics》1988,52(6):754-761
An invariant solution of the equations of gas dynamics, constructed on a one-dimensional subgroup (according to the classification in /1/) which is only allowed in the case of a polytropic gas with a special adiabatic index, is considered. The gas spreads out into a vacuum after a finite time. New solutions are constructed which describe one-dimensional flows from a source into a vacuum and the focussing of the gas within a sphere or a cylinder with shock waves. The spreading of a concentration of the gas with an arbitrary boundary when there is a contact discontinuity is also considered.
One-dimensional flows have been treated in detail in /2, 3/, mainly in the case of extended subgroups. 相似文献
3.
4.
Yuan Hongjun 《偏微分方程通讯》2013,38(5-6):965-976
In this paper, we study the one-dimensional motion of viscous gas connecting to vacuum state with a jump in density when the viscosity depends on the density. Precisely, when the viscosity coefficient μ is proportional to ρθ and 0 < θ < 1/2, where ρ is the density, the global existence and the uniqueness of weak solutions are proved. This improves the previous results by enlarging the interval of θ. 相似文献
5.
Hongjun Yuan 《Journal of Differential Equations》2008,245(10):2871-2916
The aims of this paper are to discuss existence and uniqueness of local solutions for a class of non-Newtonian fluids with singularity and vacuum in one-dimensional bounded intervals. There are two important points in this paper, one is that we allow the initial vacuum; another one is that the viscosity term of momentum equation is with singularity and fully nonlinearity. 相似文献
6.
This paper is concerned with the construction of global, large amplitude solutions to the Cauchy problem of the one-dimensional compressible Navier–Stokes system for a viscous radiative gas when the viscosity and heat conductivity coefficients depend on both specific volume and absolute temperature. The data are assumed to be without vacuum,mass concentrations, or vanishing temperatures, and the same is shown to be hold for the global solution constructed. The proof is based on some detailed analysis on uniform positive lower and upper bounds of the specific volume and absolute temperature. 相似文献
7.
n this paper,we study a free boundary value problem for two-phase liquidgas model with mass-depcndent viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously.Th... 相似文献
8.
In this paper, we proved local existence and uniqueness of solutions for a class of non-Newtonian fluids with vacuum and damping in one-dimensional bounded intervals. The main difficulty is due to the strong nonlinearity of the system and initial vacuum. 相似文献
9.
In this paper, we will investigate the global existence of solutions for the one-dimensional compressible Navier-Stokes equations when the density is in contact with vacuum continuously. More precisely, the viscosity coefficient is assumed to be a power function of density, i.e., μ(ρ)=Aρθ, where A and θ are positive constants. New global existence result is established for 0<θ<1 when the initial density appears vacuum in the interior of the gas, which is the novelty of the presentation. 相似文献
10.
Shu Wang & Fang Yuan 《偏微分方程(英文版)》2021,34(1):14-41
The aim of this paper is to explore the free boundary problem for the NonNewtonian shear thickening fluids. These fluids not only have vacuum, but also have
strong nonlinear properties. In this paper, a class of approximate solutions is first
constructed, and some uniform estimates are obtained for these approximate solutions.
Finally, the existence of free boundary problem solutions is proved by these uniform
estimates. 相似文献
11.
Dexing Kong 《偏微分方程(英文版)》1996,9(3):221-236
In this paper, we give a lower bound for the life-span of classical solutions to the Cauchy problem for first order nonlinear hyperbolic systems with small initial data, which is sharp, and give its application to the system of one-dimensional gas dynamics; for the Cauchy problem of the system of one-dimensional gas dynamics with a kind of small oscillatory initial data, we obtain a precise estimate for the life-span of classical solutions. 相似文献
12.
Tong YangHuijiang Zhao 《Journal of Differential Equations》2002,184(1):163-184
This paper is concerned with the free boundary problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. A local (in time) existence result is established when the initial density is of compact support and connects to the vacuum continuously. 相似文献
13.
Yeping LI 《数学年刊B辑(英文版)》2013,34(4):529-540
In this paper, a one-dimensional bipolar Euler-Poisson system(a hydrodynamic model) from semiconductors or plasmas with boundary efects is considered. This system takes the form of Euler-Poisson with an electric field and frictional damping added to the momentum equations. The large-time behavior of uniformly bounded weak solutions to the initial-boundary value problem for the one-dimensional bipolar Euler-Poisson system is firstly presented. Next, two particle densities and the corresponding current momenta are verified to satisfy the porous medium equation and the classical Darcy’s law time asymptotically. Finally, as a by-product, the quasineutral limit of the weak solutions to the initial-boundary value problem is investigated in the sense that the bounded L∞entropy solution to the one-dimensional bipolar Euler-Poisson system converges to that of the corresponding one-dimensional compressible Euler equations with damping exponentially fast as t → +∞. As far as we know, this is the first result about the asymptotic behavior and the quasineutral limit for the one-dimensional bipolar Euler-Poisson system with boundary efects and a vacuum. 相似文献
14.
Daoyuan Fang 《Journal of Differential Equations》2006,222(1):63-94
In this paper, we study the evolutions of the interfaces between the gas and the vacuum for viscous one-dimensional isentropic gas motions. We prove the global existence and uniqueness for discontinuous solutions of the Navier-Stokes equations for compressible flow with density-dependent viscosity coefficient. Precisely, the viscosity coefficient μ is proportional to ρθ with 0<θ<1. Specifically, we require that the initial density be piecewise smooth with arbitrarily large jump discontinuities, bounded above and below away from zero, in the interior of gas. We show that the discontinuities in the density persist for all time, and give a decay result for the density as t→+∞. 相似文献
15.
In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero. 相似文献
16.
《偏微分方程通讯》2013,38(5-6):907-943
ABSTRACT Global solutions of the multidimensional Navier-Stokes equations for compressible heat-conducting flow are constructed, with spherically symmetric initial data of large oscillation between a static solid core and a free boundary connected to a surrounding vacuum state. The free boundary connects the compressible heat-conducting fluids to the vacuum state with free normal stress and zero normal heat flux. The fluids are initially assumed to fill with a finite volume and zero density at the free boundary, and with bounded positive density and temperature between the solid core and the initial position of the free boundary. One of the main features of this problem is the singularity of solutions near the free boundary. Our approach is to combine an effective difference scheme to construct approximate solutions with the energy methods and the pointwise estimate techniques to deal with the singularity of solutions near the free boundary and to obtain the bounded estimates of the solutions and the free boundary as time evolves. The convergence of the difference scheme is established. It is also proved that no vacuum develops between the solid core and the free boundary, and the free boundary expands with finite speed. 相似文献
17.
Ansgar Jüngel 《Mathematical Methods in the Applied Sciences》1995,18(5):387-412
The quasi-hydrodynamic model for semiconductor devices in thermal equilibrium admits in general solutions for which the electron or hole density vanish. These sets are called vacuum sets. In this paper estimates on the vacuum sets and a first step in the regularity of the free boundary of these sets are presented. Numerical examples, including error estimates for linear finite elements, for the devices diode, bipolar transistor and thyristor indicate that the free boundary is more regular than theoretically predicted. 相似文献
18.
Global smooth solutions of the compressible Navier-Stokes equations with density-dependent viscosity
In this paper we study a free boundary problem for the viscous, compressible, heat conducting, one-dimensional real fluids. More precisely, the viscosity is assumed to be a power function of density, i.e., μ(ρ)=ρα, where ρ denotes the density of fluids and α is a positive constant. In addition, the equations of state include and are more general than perfect flows which only depend linearly on temperature. The global existence (uniqueness) of smooth solutions is established with for general, large initial data, which improves the previous results. Moreover, it is also shown that the solutions will not develop vacuum, mass concentration or heat concentration in a finite time provided the initial data are bounded and smooth, and do not contain vacuum. 相似文献
19.
Lei Yao 《Journal of Differential Equations》2009,247(10):2705-2519
In this paper, we study a free boundary value problem for two-phase liquid-gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum with a discontinuity. This is an extension of the paper [S. Evje, K.H. Karlsen, Global weak solutions for a viscous liquid-gas model with singular pressure law, http://www.irisresearch.no/docsent/emp.nsf/wvAnsatte/SEV]. Just as in [S. Evje, K.H. Karlsen, Global weak solutions for a viscous liquid-gas model with singular pressure law, http://www.irisresearch.no/docsent/emp.nsf/wvAnsatte/SEV], the gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We give the proof of the global existence and uniqueness of weak solutions when β∈(0,1], which have improved the previous result of Evje and Karlsen, and get the asymptotic behavior result, also we obtain the regularity of the solutions by energy method. 相似文献
20.
Global Existence of Strong Solutions of Navier-Stokes-Poisson Equations for One-Dimensional Isentropic Compressible Fluids 总被引:1,自引:1,他引:0
The authors prove two global existence results of strong solutions of the isentropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded. 相似文献