Dynamics of a modified Davey-Stewartson system in ℝ³
Jing Lu
Colloquium Mathematicae, Tome 144 (2016), p. 69-87 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We study the Cauchy problem in ℝ³ for the modified Davey-Stewartson system i∂ₜu+Δu=λ₁|u|⁴u+λ₂b₁uvx₁, -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].

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:286152 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6608-10-2015,
     author = {Jing Lu},
     title = {Dynamics of a modified Davey-Stewartson system in $\mathbb{R}$$^3$},
     journal = {Colloquium Mathematicae},
     volume = {144},
     year = {2016},
     pages = {69-87},
     zbl = {06602770},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6608-10-2015}
}

Jing Lu. Dynamics of a modified Davey-Stewartson system in ℝ³. Colloquium Mathematicae, Tome 144 (2016) pp. 69-87. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6608-10-2015/