Abstract
AbstractWe 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.
Funder
Labex CEMPI
engineering and physical sciences research council
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Physics and Astronomy,General Mathematics
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