数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (6): 2141-2160.doi: 10.1016/S0252-9602(12)60166-0

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GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

张培欣1,2|邓雪梅3|赵俊宁1   

  1. 1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
    2. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
    3. College of Science, China Three Gorges University, Yichang 443002, China
  • 收稿日期:2011-07-04 出版日期:2012-11-20 发布日期:2012-11-20
  • 基金资助:

    This work was partially supported by National Natural Science Foundation of China (11001090) and the Fundamental Research Funds for the Central Universities (11QZR16).

GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

 ZHANG Pei-Xin1,2, DENG Xue-Mei3, ZHAO Jun-Ning1   

  1. 1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
    2. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
    3. College of Science, China Three Gorges University, Yichang 443002, China
  • Received:2011-07-04 Online:2012-11-20 Published:2012-11-20
  • Supported by:

    This work was partially supported by National Natural Science Foundation of China (11001090) and the Fundamental Research Funds for the Central Universities (11QZR16).

摘要:

We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ||ρ0||L is appropriate small and 1 << 6/ 5 . Here the initial density could have vacuum and we do not require that the initial energy is small.

关键词: compressible Navier-Stokes equations, global classical solutions, general ini-tial energy

Abstract:

We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ||ρ0||L is appropriate small and 1 << 6/ 5 . Here the initial density could have vacuum and we do not require that the initial energy is small.

Key words: compressible Navier-Stokes equations, global classical solutions, general ini-tial energy

中图分类号: 

  • 76N10