Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (5): 1111-1122.

• Articles • Previous Articles     Next Articles

The Global Solutions of the Compressible Euler Equations With Nonlinear Damping in 3-Dimensions

 ZHU Xu-Sheng, LI Fang-E   

  1. 1.School of Basic Science, East China Jiaotong University, Nanchang, 330013;
    2.Xinxiang No.1 High Sschool, Henan Xinxiang, 453000
  • Received:2013-04-08 Revised:2014-03-17 Online:2014-10-25 Published:2014-10-25
  • Supported by:

    国家自然科学基金(11161021, 61262031)和江西省高校科技落地计划项目(KJLD12067)资助.

Abstract:

The Cauchy problem for the compressible isentropic Euler equations with nonlinear damping in three space dimensions is investigated in this paper. The global classic solution is obtained provided the initial data is a small perturbation in H3L1 of a constant state by utilizing energy estimates, the L2, L decays rates of the global solution are also obtained by using Fourier transform method, they are t-3/4, t-3/2 respectively. Here we have generalized the linear damping case to nonlinear damping case.

Key words: The compressible Euler equations, Nonlinear damping, Global solutions, Decay estimates

CLC Number: 

  • 35L45
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