Density-dependent Viscosity Coefficients Research Articles

Free Boundary Value Problem for the Spherically Symmetric Compressible Navier-Stokes Equations with a Nonconstant Exterior Pressure

This paper is concerned with the free boundary value problem (FBVP) for the spherically symmetric barotropic compressible Navier-Stokes equations (CNS) with density-dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a nonconstant exterior pressure. Under certain assumptions imposed on the initial data, we show that there exists a unique global strong solution which is strictly positive for any finite time and decays pointwise to zero time-asymptotically.

Free boundary value problem for the cylindrically symmetric compressible navier-stokes equations with density-dependent viscosity

In this paper, we investigate the free boundary value problem (FBVP) for the cylindrically symmetric isentropic compressible Navier-Stokes equations (CNS) with density-dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.

Global strong solutions to the vacuum free boundary problem for compressible Navier–Stokes equations with degenerate viscosity and gravity force

For the vacuum free boundary problem of the one-dimensional compressible Navier–Stokes equations with the density dependent viscosity coefficient and gravity force, the global existence of the strong solution is proved, which is shown to converge to the steady solution with the same total mass when the initial datum is a small perturbation of the steady solution only at the basic level. The key is to establish the global-in-time regularity uniformly up to the vacuum boundary, which ensures the large time asymptotic uniform convergence of the evolving vacuum boundary, density and velocity to those of the steady solution with detailed convergence rates. Compared with previous studies, the novelty of this paper is the regularity of global solutions for the vacuum free boundary problems in viscous compressible fluids when the viscosity coefficient is not constant but degenerate.

Global existence of weak solution for the compressible Navier–Stokes–Poisson system for gaseous stars

We study the multi-dimensional compressible Navier–Stokes–Poisson system with γ-law pressure and density-dependent viscosity coefficients in the simulation of the motion of gaseous stars. The global existence of spherically symmetric weak solutions to the free boundary value problem for the Navier–Stokes–Poisson system for γ∈(65,43] is shown for arbitrarily large initial data with compact support.

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

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 $h(\rho)=\mu\geq0$ , and the bulk viscosity $g(\rho)=\rho^{\beta}$ ( $\beta>0$ ). By constructing a class of radial symmetric and self-similar analytical solutions in $\mathbb {R}^{N}$ ( $N\geq2$ ) 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.

Global classical solutions to the one-dimensional compressible fluid models of Korteweg type with large initial data

This paper is concerned with the global existence of classical solutions with large initial data away from vacuum to the Cauchy problem of the one-dimensional isothermal compressible fluid models of Korteweg type with density-dependent viscosity coefficient and capillarity coefficient. The case when the viscosity coefficient μ(ρ)=ρα and the capillarity coefficient κ(ρ)=ρβ for some parameters α,β∈R is considered. Under some conditions on α,β, we first show the global existence of large solutions around constant states if the far-fields of the initial data are the same, while if the far-fields of the initial data are different, we prove the global stability of rarefaction waves with large strength. Here global stability means the initial perturbation can be arbitrarily large. Our analysis is based on the elementary energy method and the technique developed by Y. Kanel' [29].

Global well-posedness for the incompressible Navier–Stokes equations with density-dependent viscosity coefficient

This paper is concerned with an initial–boundary value problem of the incompressible Navier–Stokes equations with density-dependent viscosity in a smooth bounded domain Ω⊂R3. The global well-posedness of strong solutions with large oscillations is established in both non-vacuum and vacuum cases, provided the initial velocity is suitably small in certain sense. It is worth pointing out that there isn't any smallness condition on the density and its gradient.

On the free boundary value problem for one-dimensional compressible Navier-Stokes equations with constant exterior pressure

In this paper, we consider the free boundary value problem (FBVP) for one-dimensional isentropic compressible Navier-Stokes equations (CNS) with density-dependent viscosity coefficient and constant exterior pressure. Under certain assumptions imposed on the initial data, the global existence and uniqueness of a strong solution to FBVP for CNS are established, in particular, the strong solution tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.

Approximate solutions to a model of two-component reactive flow

We consider a model of motion of binary mixture, based on the compressible Navier-Stokes system. The mass balances of chemically reacting species are described by the reaction-diffusion equations with generalized form of multicomponent diffusion flux. Under a special relation between the two density dependent viscosity coefficients and for singular cold pressure we construct the weak solutions passing through several levels of approximation.

Global classical solution to the 3D isentropic compressible Navier-Stokes equations with general initial data and a density-dependent viscosity coefficient

In this paper, we study the global existence of classical solutions to the three-dimensional compressible Navier–Stokes equations with a density-dependent viscosity coefficient (λ = λ(ρ)). For the general initial data, which could be either vacuum or non-vacuum, we prove the global existence of classical solutions, under the assumption that the viscosity coefficient μ is large enough. Copyright © 2014 John Wiley & Sons, Ltd.

A Lagrangian approach for the compressible Navier-Stokes equations

Here we investigate the Cauchy problem for the barotropic Navier-Stokes equations in ℝ n , in the critical Besov spaces setting. We improve recent results as regards the uniqueness condition: initial velocities in critical Besov spaces with (not too) negative indices generate a unique local solution. Apart from (critical) regularity, the initial density just has to be bounded away from 0 and to tend to some positive constant at infinity. Density-dependent viscosity coefficients may be considered. Using Lagrangian coordinates is the key to our statements as it enables us to solve the system by means of the basic contraction mapping theorem. As a consequence, conditions for uniqueness are the same as for existence, and Lipschitz continuity of the flow map (in Lagrangian coordinates) is established.

Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with a Nonconstant Exterior Pressure

We consider the free boundary value problem (FBVP) for one-dimensional isentropic compressible Navier-Stokes (CNS) equations with density-dependent viscosity coefficient in the case that across the free surface stress tensor is balanced by a nonconstant exterior pressure. Under certain assumptions imposed on the initial data and exterior pressure, we prove that there exists a unique global strong solution which is strictly positive from blow for any finite time and decays pointwise to zero at an algebraic time-rate.

Global Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data

We consider the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data in this paper. For piecewise regular initial density with bounded jump discontinuity, we show that there exists a unique global piecewise regular solution. In particular, the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially ast→+∞.

Free boundary value problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity

We study the free boundary value problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient in this paper. Under certain assumptions imposed on the initial data, we show that there exists a unique global strong solution, the interface separating the flow and vacuum state propagates along particle path and expands outwards at an algebraic time-rate, the flow density is strictly positive from blow for any finite time and decays pointwise to zero also at an algebraic time-rate as the time tends to infinity.

Blowup of solutions for the compressible Navier–Stokes equations with density-dependent viscosity coefficients

We study the blowup phenomena of solutions to the compressible Navier–Stokes equations with density-dependent viscosity coefficients in arbitrary dimensions. By constructing a family of self-similar analytical solutions with spherical symmetry, some interesting information including the blowup and expanding properties are shown. In addition, the case of constant viscosity coefficients is also considered. The approach is based on the phase plane method.

Existence of global strong solutions for Navier–Stokes equations with external force

We consider the initial boundary value problems (IBVPs) for 1D isentropic compressible Navier–Stokes equations with density-dependent viscosity coefficients and external force. If the initial data is regular, the existence and uniqueness of global strong solution to IBVP are proved in this article.

Global solution to the exterior problem for spherically symmetric compressible Navier-Stokes equations with density-dependent viscosity and discontinuous initial data

In this paper, we consider the exterior problem for spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data. We prove that there exists a unique global piecewise regular solution for piecewise regular initial density with bounded jump discontinuity. In particular, the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially as .

Time-discretized steady compressible Navier–Stokes equations with inflow and outflow boundaries

The time-discretized steady compressible Navier–Stokes equations in n-dimensional bounded domains with the velocity specified only at the inflow boundary are considered. The existence and uniqueness of L p solutions are proved for p > n. For time-discretized steady flows, results of Kweon and Kellogg and of Kweon and Song are extended in a manner that allows for more general domains and for density-dependent viscosity coefficients. Moreover, we only require p > n which is a critical barrier in the previous works.

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

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 (λ=λ(ρ)) 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.

Global Solutions to the One-Dimensional Compressible Navier--Stokes--Poisson Equations with Large Data

In this paper, we study the global solutions with large data away from vacuum to the Cauchy problem of the one-dimensional compressible Navier--Stokes--Poisson system with density-dependent viscosity coefficient and density- and temperature-dependent heat-conductivity coefficient. The proof is based on some detailed analysis on the bounds on the density and temperature functions.