Blow-up results for systems of nonlinear Schrödinger 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.

22 pages, minor changes. Zeitschrift für angewandte Mathematik und Physik (ZAMP), to appear

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