| Texto completo | |
| Autor(es): |
Campos, Luccas
;
Pastor, Ademir
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | SIAM JOURNAL ON MATHEMATICAL ANALYSIS; v. 57, n. 6, p. 31-pg., 2025-12-31. |
| Resumo | |
We consider the Schrodinger system { i partial derivative(t)u+Delta u+ (| u| (2)+beta| v| (2))u= 0, i partial derivative(t)v+Delta v+ (| v| (2)+beta| u| (2))v= 0, with initial data (u(0),v(0))is an element of H-1(R (3)) X H-1(R (3)) at the so-called mass-energy threshold ,i.e., such that M(u(0),v(0))E(u(0),v(0)) =M(Phi,psi)E(Phi,psi), where (Phi,psi ) is a ground state. For a suitable range of values of beta > 0, we show the existence of special solutions to this system, which converge to a standing wave solution in one time direction, and either blow up or scatters in the opposite direction. Moreover, we classify general solutions at the ground state, showing a rigidity result regarding the possible long-time behaviors that might occur. Our results do not rely on the uniqueness of the corresponding ground state; indeed, the main results hold even in the case where the Weinstein functional is known to have more than one optimizer. (AU) | |
| Processo FAPESP: | 19/02512-5 - Sistemas e equações diferenciais parciais |
| Beneficiário: | Marcelo da Silva Montenegro |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 20/10185-1 - Comportamento local e global de soluções de equações dispersivas |
| Beneficiário: | Luccas Cassimiro Campos |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |