| Texto completo | |
| Autor(es): |
Hespanha, Maicon
;
Pastor, Ademir
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | STUDIES IN APPLIED MATHEMATICS; v. 154, n. 3, p. 18-pg., 2025-03-01. |
| Resumo | |
This paper is concerned with a cubic nonlinear Schr & ouml;dinger system modeling the interaction between an optical beam and its third harmonic in a material with Kerr-type nonlinear response. We are mainly interested in the so-called energy-critical case, that is, in dimension four. Our main result states that radially symmetric solutions with initial energy below that of the ground states but with kinetic energy above that of the ground states must blow up in finite time. The proof of this result is based on the convexity method. As an independent interest we also establish the existence of ground state solutions, that is, solutions that minimize some action functional. In order to obtain our existence results, we use the concentration-compactness method combined with variational arguments. As a byproduct, we also obtain the best constant in a vector-critical Sobolev-type inequality. (AU) | |
| Processo FAPESP: | 19/02512-5 - Sistemas e equações diferenciais parciais |
| Beneficiário: | Marcelo da Silva Montenegro |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |