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 IJMNTA  Vol.5 No.3 , September 2016
On the Stability of the Defocusing Mass-Critical Nonlinear Schrödinger Equation
Abstract: We consider the defocusing mass-critical nonlinear Schr?dinger equation in the exterior domain in (). By analyzing Strichartz estimate and utilizing the inductive hypothesis method, we prove the stability for all initial data in .
Cite this paper: Zhang, G. (2016) On the Stability of the Defocusing Mass-Critical Nonlinear Schrödinger Equation. International Journal of Modern Nonlinear Theory and Application, 5, 115-121. doi: 10.4236/ijmnta.2016.53012.
References

[1]   Brezis, H. and Gallouet, T. (1980) Nonlinear Schrödinger Evolution Equations. Nonlinear Analysis, 4, 677-681.

[2]   Burq, N., Gérard, P. and Tzvetkov, N. (2004) On Nonlinear Schrödinger Equations in Exterior Domains. Annales de l’Institut Henri Poincaré (C) Analyse Non Linear Analysis, 21, 295-318.

[3]   Killip, R., Visan, M. and Zhang, X. (2012) Quintic NLS in the Exterior of a Strictly Convex Obstacle. Mathematics. arXiv:1208.4904.

[4]   Killip, R., Visan, M. and Zhang, X. (2015) The Focusing Cubic NLS on Exterior Domains in Three Dimensions. Mathematics, 89, 335-354.

[5]   Tao, T. and Visan, M. (2005) Stability of Energy-Critical Nonlinear Schrödinger Equations in High Dimensions. Electronic Journal of Differential Equations, 2, 357-370.

[6]   Keel, M. and Tao, T. (1997) Endpoint Strichartz Estimates. American Journal of Mathematics, 120, 955-980.

 
 
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