# Blow up of solutions to the nonlinear Schroedinger equations on manifolds

## Abstract

In this paper, we partially settle down the long-standing open problem of the finite time blow-up property about the nonlinear Schroedinger equations on some Riemannian manifolds such as the standard 2-sphere S{sup 2} and the hyperbolic 2-space H{sup 2}(-1). Using the similar idea, we establish such blow-up results on higher dimensional standard sphere and hyperbolic n-space. Extensions to n-dimensional Riemannian warped product manifolds with n{>=}2 are also given.

- Authors:

- Department of Mathematical Sciences, Tsinghua University, Peking 100084 (China)

- Publication Date:

- OSTI Identifier:
- 20929727

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 5; Other Information: DOI: 10.1063/1.2722560; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MATHEMATICAL MANIFOLDS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; NONLINEAR PROBLEMS; SCHROEDINGER EQUATION; SPHERES

### Citation Formats

```
Ma Li, and Zhao Lin.
```*Blow up of solutions to the nonlinear Schroedinger equations on manifolds*. United States: N. p., 2007.
Web. doi:10.1063/1.2722560.

```
Ma Li, & Zhao Lin.
```*Blow up of solutions to the nonlinear Schroedinger equations on manifolds*. United States. doi:10.1063/1.2722560.

```
Ma Li, and Zhao Lin. Tue .
"Blow up of solutions to the nonlinear Schroedinger equations on manifolds". United States.
doi:10.1063/1.2722560.
```

```
@article{osti_20929727,
```

title = {Blow up of solutions to the nonlinear Schroedinger equations on manifolds},

author = {Ma Li and Zhao Lin},

abstractNote = {In this paper, we partially settle down the long-standing open problem of the finite time blow-up property about the nonlinear Schroedinger equations on some Riemannian manifolds such as the standard 2-sphere S{sup 2} and the hyperbolic 2-space H{sup 2}(-1). Using the similar idea, we establish such blow-up results on higher dimensional standard sphere and hyperbolic n-space. Extensions to n-dimensional Riemannian warped product manifolds with n{>=}2 are also given.},

doi = {10.1063/1.2722560},

journal = {Journal of Mathematical Physics},

number = 5,

volume = 48,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2722560

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