Dynamics of a modified Davey-Stewartson system in ℝ³

• Autorzy: Jing Lu
• Języki publikacji: EN

Abstrakty

EN

We study the Cauchy problem in ℝ³ for the modified Davey-Stewartson system
$i∂ₜu + Δu = λ₁|u|⁴u + λ₂b₁uv_{x₁}$, $-Δv = b₂(|u|²)_{x₁}$.
Under certain conditions on λ₁ and λ₂, we provide a complete picture of the local and global well-posedness, scattering and blow-up of the solutions in the energy space. Methods used in the paper are based upon the perturbation theory from [Tao et al., Comm. Partial Differential Equations 32 (2007), 1281-1343] and the convexity method from [Glassey, J. Math. Phys. 18 (1977), 1794-1797].

Kategorie tematyczne

• 47J35: Nonlinear evolution equations
• 35Q53: KdV-like equations (Korteweg-de Vries)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 145
• Numer: 1
• Strony: 69-87

Daty

wydano

2016

Twórcy

autor

Jing Lu

• China Academy of Engineering Physics, Beijing, 100088, China

Identyfikatory

DOI

10.4064/cm6608-10-2015