Geodesic
Dynamics of a modified Davey–Stewartson system in $\mathbb {R}^3$
Jing Lu 1
1 China Academy of Engineering Physics Beijing, 100088, China
Colloquium Mathematicum, Tome 145 (2016) no. 1, pp. 69-87 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the Cauchy problem in $\mathbb {R}^3$ for the modified Davey–Stewartson system $$ i\partial _t u + \varDelta u =\lambda _1|u|^{4}u+\lambda _2b_1uv_{x_1},\hskip 1em -\varDelta v=b_2(|u|^2)_{x_1}. $$ Under certain conditions on $\lambda _1$ and $\lambda _2$, 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].
DOI : 10.4064/cm6608-10-2015
Keywords: study cauchy problem mathbb modified davey stewartson system partial vardelta lambda lambda hskip vardelta under certain conditions nbsp lambda nbsp nbsp lambda provide complete picture local global well posedness scattering blow up solutions energy space methods paper based perturbation theory tao comm partial differential equations convexity method glassey nbsp math phys

Jing Lu  1

1 China Academy of Engineering Physics Beijing, 100088, China 
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Jing Lu. Dynamics of a modified Davey–Stewartson system in $\mathbb {R}^3$. Colloquium Mathematicum, Tome 145 (2016) no. 1, pp. 69-87. doi: 10.4064/cm6608-10-2015

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