The growth in time of higher Sobolev norms of solutions to Schrödinger equations on compact Riemannian manifolds

Journal of Differential Equations ◽

10.1016/j.jde.2008.03.008 ◽

2008 ◽

Vol 245 (2) ◽

pp. 359-376 ◽

Author(s):

Sijia Zhong

Keyword(s):

Riemannian Manifolds ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Download Full-text

Pointwise Carleman estimates, global uniqueness, observability, and stabilization for Schrödinger equations on Riemannian manifolds at the 𝐻¹(Ω)-level

Control Methods in PDE-Dynamical Systems - Contemporary Mathematics ◽

10.1090/conm/426/08197 ◽

2007 ◽

pp. 339-404 ◽

Author(s):

Roberto Triggiani ◽

Xiangjin Xu

Keyword(s):

Riemannian Manifolds ◽

Carleman Estimates ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Global Uniqueness

Download Full-text

On growth in time of Sobolev norms of smooth solutions of nonlinear Schrödinger equations in ℝD

Journal d Analyse Mathématique ◽

10.1007/bf02843163 ◽

1997 ◽

Vol 72 (1) ◽

pp. 299-310 ◽

Author(s):

J. Bourgain

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Smooth Solutions ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Download Full-text

On growth of Sobolev norms in time dependent linear Schrödinger equations on spheres

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2012.01.029 ◽

2012 ◽

Vol 390 (1) ◽

pp. 165-180

Author(s):

Qidi Zhang ◽

Daoyuan Fang

Keyword(s):

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Download Full-text

Growth of Sobolev Norms of Solutions of Linear Schrodinger Equations on Some Compact Manifolds

International Mathematics Research Notices ◽

10.1093/imrn/rnp213 ◽

2009 ◽

Author(s):

J.-M. Delort

Keyword(s):

Compact Manifolds ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Download Full-text

Global smooth solutions for semilinear Schrödinger equations with boundary feedback on 2-dimensional Riemannian manifolds

Journal of Systems Science and Complexity ◽

10.1007/s11424-009-9199-x ◽

2009 ◽

Vol 22 (4) ◽

pp. 749-776 ◽

Author(s):

Li Deng ◽

Pengfei Yao

Keyword(s):

Riemannian Manifolds ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Smooth Solutions ◽

Boundary Feedback ◽

Global Smooth Solutions

Download Full-text

Growth of Sobolev Norms in Linear Schrödinger Equations with Quasi-Periodic Potential

Communications in Mathematical Physics ◽

10.1007/s002200050644 ◽

1999 ◽

Vol 204 (1) ◽

pp. 207-247 ◽

Author(s):

J. Bourgain

Keyword(s):

Periodic Potential ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Download Full-text

Growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential

Global Solutions of Nonlinear Schrödinger Equations - Colloquium Publications ◽

10.1090/coll/046/07 ◽

1999 ◽

pp. 155-172

Keyword(s):

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Sobolev Norms ◽

Dependent Potential

Download Full-text

On the growth of Sobolev norms for a class of linear Schrödinger equations on the torus with superlinear dispersion

Asymptotic Analysis ◽

10.3233/asy-181470 ◽

2018 ◽

Vol 108 (1-2) ◽

pp. 85-114 ◽

Author(s):

Riccardo Montalto

Keyword(s):

Schrodinger Equations ◽

Schrödinger Equations ◽

Download Full-text

Lower bounds on the growth of Sobolev norms in some linear time dependent Schrödinger equations

Mathematical Research Letters ◽

10.4310/mrl.2019.v26.n4.a11 ◽

2019 ◽

Vol 26 (4) ◽

pp. 1197-1215 ◽

Author(s):

Alberto Maspero

Keyword(s):

Lower Bounds ◽

Linear Time ◽

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Download Full-text

Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on \begin{document}$ h\mathbb{Z} $\end{document}

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2019131 ◽

2019 ◽

Vol 39 (6) ◽

pp. 3179-3195 ◽

Author(s):

Joackim Bernier ◽

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations ◽

Download Full-text