Local Well-Posedness for the Davey–Stewartson Equation in a Generalized Feichtinger Algebra

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• 作者：Mitsuru Sugimoto ; Baoxiang Wang…
• 关键词：Davey–Stewartson equations ; Local well ; posedness ; Feichtinger algebra ; 35Q55 ; 42B35 ; 42B37
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：21
• 期：5
• 页码：1105-1129
• 全文大小：753 KB
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• 作者单位：Mitsuru Sugimoto (1)
  Baoxiang Wang (2)
  Rongrong Zhang (2)
  
  1. Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8062, Japan
  2. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Fourier Analysis
  Abstract Harmonic Analysis
  Approximations and Expansions
  Partial Differential Equations
  Applications of Mathematics
  Signal,Image and Speech Processing
  
• 出版者：Birkh盲user Boston
• ISSN：1531-5851

文摘

In this paper, we consider the initial value problem for the hyperbolic-type Davey–Stewartson equations, including elliptic–hyperbolic and hyperbolic–hyperbolic cases. We show the local existence and uniqueness of the solution in the generalized Feichtinger algebra \(\breve{M}_{1,1}^{s}(s\ge 3/2)\) with sufficiently small initial data in \(\breve{M}^{3/2}_{1,1}(\mathbb {R}^{2})\). Moreover, we show the ill-posedness of the solutions in the sense that the solution map is not \(C^3\) if the spatial regularity is below \(\breve{M}_{1,1}^{3/2}\). Keywords Davey–Stewartson equations Local well-posedness Feichtinger algebra