Asymptotic Behavior of Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum

作者：Zhu, Changjiang^*

来源：Communications in Mathematical Physics, 2010, 293(1): 279-299.

DOI：10.1007/s00220-009-0914-1

• DISCONTINUOUS INITIAL DATA
• ONE-DIMENSIONAL EQUATIONS
• GLOBAL WEAK SOLUTIONS
• VISCOUS-GAS
• SMOOTH SOLUTIONS
• FLOW
• FLUID
• MOTION
• CONVERGENCE
• COEFFICIENT

In this paper, we study the one-dimensional Navier-Stokes equations connecting to vacuum state with a jump in density when the viscosity depends on the density. Precisely, when the viscosity coefficient mu(rho) is proportional to rho (theta) with theta > 0, where rho is the density, we give the asymptotic behavior and the decay rate of the density function rho(x, t). Furthermore, the behavior of the density function rho(x, t) near the interfaces separating the gas from vacuum and the expanding rate of the interfaces are also studied. The analysis is based on some new mathematical techniques and some new useful estimates. This fills a final gap on studying Navier-Stokes equations with the viscosity coefficient mu(rho) dependent on the density rho.

• 出版日期2010-1
• 单位华中师范大学