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Solvability of the Cauchy problem of non-isotropic Schrödinger equations in Sobolev spaces

✍ Scribed by Cuihua Guo; Shangbin Cui

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
274 KB
Volume
68
Category
Article
ISSN
0362-546X

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✦ Synopsis

We study the existence of solutions for the Cauchy problem of the non-isotropically perturbed nonlinear Schrödinger equation

where a, b are not simultaneously vanishing real constants, α is a positive constant, and x = (x 1 , x 2 ) ∈ R 2 . By using Kato's method, we establish some local existence results for initial data belonging to

Global existence is also established under some additional conditions.

📜 SIMILAR VOLUMES

Nonlinear Schrödinger Equations in the S
Nonlinear Schrödinger Equations in the Sobolev Space of Critical Order
✍ M Nakamura; T Ozawa 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 310 KB

The Cauchy problem for the nonlinear Schro dinger equations is considered in the Sobolev space H nÂ2 (R n ) of critical order nÂ2, where the embedding into L (R n ) breaks down and any power behavior of interaction works as a subcritical nonlinearity. Under the interaction of exponential type the ex