The Existence of Global Solutions to Systems of Quasilinear Wave Equations with Quadratic Nonlinearities in 2-Dimensional Space

• Hoshiga Akira

  Shizuoka University

Abstract

We deal with systems of quasilinear wave equations which contain quadratic nonlinearities in 2-dimensional space. We have already known that such the system has a smooth solution till the time t₀ = Cε^-2 for sufficiently small ε > 0, where ε is the size of initial data. In this paper, we shall show that if quadratic and cubic nonlinearities satisfy so-called Null-condition, then the smooth solution exists globally in time. In the proof of the theorem, we use the Alinhac ghost weight energy.

Journal

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 49 (3), 357-384, 2006

  Division of Functional Equations, The Mathematical Society of Japan

Keywords

• Null-form
• Multiple speeds
• Global existence

Details

• CRID: 1390001205112993664
• NII Article ID: 130000140672
• DOI: 10.1619/fesi.49.357
• ISSN: 05328721
• Web Site: http://www.jstage.jst.go.jp/article/fesi/49/3/49_3_357/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed