CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

• 作 者: Lian Ruxu Liu Jian Li Hailiang
• 机 构: College of Mathematics and Information Science,Department of Mathematics,Academy of Mathematics and
• 出 处: 数学物理学报（英文版）
• 发表日期: 2004年期
• 关键词: Navier-Stokes equations discontinuous initial data
• 基金项目: the Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality;the Huo Ying Dong Fund;The research of H.L.Li is partially suppor

We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient.For regular initial data,we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically.When initial density is piecewise regular with jump discontinuity,we show that there exists a unique global piecewise regular solution. In particular,the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t→ +∞.