| 初值间断的Navier-Stokes方程柯西问题弱解的存在性 |
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| 作者单位： | ;1.北京大学光华管理学院;2.首都师范大学数学科学学院;3.西安电子科技大学计算机学院;4.华北水利水电大学数学与信息科学学院 |
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| 摘 要： | 主要研究了初值间断的一维可压缩Navier-Stokes方程的柯西问题.当初始密度间断任意大时,证明了黏性系数依赖密度的一维可压缩Navier-Stokes方程柯西问题整体弱解的存在性、分段正则性.并证明了密度的跳跃间断以指数速率衰减到零,同时弱解也趋于平衡态等.
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| 关 键 词： | Navier-Stokes方程 柯西问题 初值间断 弱解 |
Cauchy Problem for One-dimensional Barotropic Compressible Navier-Stokes Equations with Density-dependent Viscosity and Discontinuous Initial Data |
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| Institution: | ,Guanghua School of Management Peking University,School of Mathematical Sciences Capital Normal University,School of Computer Science and Technology Xidian University,School of Mathematics and Information Science North China University of Water Resources and Electric Power |
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| Abstract: | This paper is concerned with the Cauchy problem for one-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosity coefficient and discontinuous initial data.For the Cauchy problem,we prove that there exists a unique global piecewise regular solution for piecewise regular initial density with arbitrarily large jump discontinuity.Moreover,we show that the jump of density decays exponentially in time and the piecewise regular solution also decays as time tends to infinity. |
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| Keywords: | Navier-Stokes equations Cauchy problem discontinuous initial data weak solution |
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