Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction

Van Duong Dinh; Luigi Forcella

doi:10.1007/s00033-021-01607-6

Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction

Van Duong Dinh, Luigi Forcella^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

61 Downloads (Pure)

Abstract

We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetric solutions. With our construction, we moreover prove some polynomial lower bounds on the kinetic energy of global solutions in the mass-critical case, which in turn implies grow-up along any diverging time sequence. Our analysis extends to general NLS systems with quadratic interactions, and it also provides improvements of known results in the radial case.

Original language	English
Article number	178
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	72
Issue number	5
Early online date	4 Sept 2021
DOIs	https://doi.org/10.1007/s00033-021-01607-6
Publication status	Published - Oct 2021

Keywords

Blow-up
Grow-up
Nonlinear Schrödinger systems
Quadratic-type interactions

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy
Applied Mathematics

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title = "Blow-up results for systems of nonlinear Schr{\"o}dinger equations with quadratic interaction",

abstract = "We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetric solutions. With our construction, we moreover prove some polynomial lower bounds on the kinetic energy of global solutions in the mass-critical case, which in turn implies grow-up along any diverging time sequence. Our analysis extends to general NLS systems with quadratic interactions, and it also provides improvements of known results in the radial case.",

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AU - Forcella, Luigi

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N2 - We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetric solutions. With our construction, we moreover prove some polynomial lower bounds on the kinetic energy of global solutions in the mass-critical case, which in turn implies grow-up along any diverging time sequence. Our analysis extends to general NLS systems with quadratic interactions, and it also provides improvements of known results in the radial case.

AB - We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetric solutions. With our construction, we moreover prove some polynomial lower bounds on the kinetic energy of global solutions in the mass-critical case, which in turn implies grow-up along any diverging time sequence. Our analysis extends to general NLS systems with quadratic interactions, and it also provides improvements of known results in the radial case.

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KW - Quadratic-type interactions

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Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction

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