数学季刊 ›› 2006, Vol. 21 ›› Issue (1): 49-56.

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半线性波动方程解的低正则局部存在性

  

  1. Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
  • 收稿日期:2005-04-06 出版日期:2006-03-30 发布日期:2023-12-19
  • 作者简介:YANG Ning(1957-),male,native of Chengdu,Sichuan,a professor of Southwest Jiaotong University,M.S.D.,engages in partial differential equations.
  • 基金资助:
    Supported by the NSF of China(10225102,10301026);Supported by the South-west Jiaotong University Foundation(20005B05)

Existence for Semilinear Wave Equations with Low Regularity

  1. Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
  • Received:2005-04-06 Online:2006-03-30 Published:2023-12-19
  • About author:YANG Ning(1957-),male,native of Chengdu,Sichuan,a professor of Southwest Jiaotong University,M.S.D.,engages in partial differential equations.
  • Supported by:
    Supported by the NSF of China(10225102,10301026);Supported by the South-west Jiaotong University Foundation(20005B05)

摘要:  In this paper,we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations …. We proved that the range of s is ,respectively,with if  n=2, and δ>0 if n=3, and δ≥0 if n≥4. Which  is  consistent   with  Lindblad's  counterexamples [3] for n=3, and the main ingredient is the use of the Strichartz estimates and the refinement of these.

关键词: semilinear wave equations, local existence, low regularity

Abstract:  In this paper,we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations …. We proved that the range of s is ,respectively,with if  n=2, and δ>0 if n=3, and δ≥0 if n≥4. Which  is  consistent   with  Lindblad's  counterexamples [3] for n=3, and the main ingredient is the use of the Strichartz estimates and the refinement of these.

Key words: semilinear wave equations, local existence, low regularity

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