Dynamics of a modified Davey-Stewartson system in ℝ³

Jing Lu

Colloquium Mathematicae (2016)

  • Volume: 145, Issue: 1, page 69-87
  • ISSN: 0010-1354

Abstract

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We study the Cauchy problem in ℝ³ for the modified Davey-Stewartson system i ∂ ₜ u + Δ u = λ ₁ | u | ⁴ u + λ ₂ b ₁ u v x ₁ , - Δ v = b ₂ ( | u | ² ) x ₁ . 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].

How to cite

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Jing Lu. "Dynamics of a modified Davey-Stewartson system in ℝ³." Colloquium Mathematicae 145.1 (2016): 69-87. <http://eudml.org/doc/286152>.

@article{JingLu2016,
abstract = {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].},
author = {Jing Lu},
journal = {Colloquium Mathematicae},
keywords = {Davey-Stewartson system; scattering; global well-posedness; blowup},
language = {eng},
number = {1},
pages = {69-87},
title = {Dynamics of a modified Davey-Stewartson system in ℝ³},
url = {http://eudml.org/doc/286152},
volume = {145},
year = {2016},
}

TY - JOUR
AU - Jing Lu
TI - Dynamics of a modified Davey-Stewartson system in ℝ³
JO - Colloquium Mathematicae
PY - 2016
VL - 145
IS - 1
SP - 69
EP - 87
AB - 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].
LA - eng
KW - Davey-Stewartson system; scattering; global well-posedness; blowup
UR - http://eudml.org/doc/286152
ER -

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