Compressible Flows with a Density-Dependent Viscosity Coefficient
نویسندگان
چکیده
We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient (λ = λ(ρ)). Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. Then, we show that if there is a vacuum domain at the initial time, then the vacuum domain will retain for all time, and vanishes as time goes to infinity. At last, we show that the condition of μ =constant will induce a singularity of the system at vacuum. Thus, the viscosity coefficient μ plays a key role in the Navier-Stokes equations.
منابع مشابه
ar X iv : 0 90 1 . 03 52 v 2 [ m at h . A P ] 1 3 Fe b 20 09 Compressible flows with a density - dependent viscosity coefficient ∗
We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient (λ = λ(ρ)). Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. Then, we show that if there is a vacuum domain at the initial time, then the vacuum domain will retain for all time, and vanish...
متن کاملGlobal Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations with Density-Dependent Viscosity
We consider the exterior problem and the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient in this paper. For regular initial density, we show that there exists a unique global strong solution to the exterior problem or the initial boundary value problem, respectively. In particular, the stro...
متن کاملAn example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
Abstract The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on x. This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence ...
متن کاملGlobal Solutions to the One-Dimensional Compressible Navier-Stokes-Poisson Equations with Large Data
This paper is concerned with the construction of global smooth solutions away from vacuum to the Cauchy problem of the one-dimensional compressible Navier-Stokes-Poisson system with large data and 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 f...
متن کاملGlobal solutions of compressible Navier–Stokes equations with a density–dependent viscosity coefficient
We prove the global existence and uniqueness of the classical (weak) solution for the 2D or 3D compressible Navier–Stokes equations with a density–dependent viscosity coefficient (λ = λ(ρ)). Initial data and solutions are only small in the energy-norm. We also give a description of the large time behavior of the solution. Then, we study the propagation of singularities in solutions. We obtain t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Math. Analysis
دوره 41 شماره
صفحات -
تاریخ انتشار 2009