Existence of global solutions for a class of vector fields on the three-dimensional torus

Autor(es)

Bergamasco, Adalberto P. ^[1] ; Dattori da Silva, Paulo L. ^[1] ; Gonzalez, Rafael B. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Estadual Maringa, Dept Matemat, BR-87020900 Maringa, PR - Brazil

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN DES SCIENCES MATHEMATIQUES; v. 148, p. 53-76, OCT 2018.
• Citações Web of Science: 0

Resumo

This work deals with global solvability of a class of vector fields of the form L = partial derivative/partial derivative t + (a(x) + ib(x)) (partial derivative/partial derivative x + lambda partial derivative/partial derivative y), where a, b is an element of C-infinity(T-1, R) and lambda is an element of R, defined on the three-dimensional torus T-3 (x, y, t) similar or equal to R-3/2 pi Z(3). In addition to the interplay between the order of vanishing of the functions a and b, the change of sign of b between two consecutive zeros of a + ib has influence in the global solvability. Also, a Diophantine condition appears in a natural way in our results. (C) 2018 Elsevier Masson SAS. All rights reserved. (AU)

• Processo FAPESP: 12/03168-7 - Teoria geométrica de EDP e várias variáveis complexas
• Beneficiário: Jorge Guillermo Hounie
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 10/52274-9 - Resolubilidade global no toro n-dimensional
• Beneficiário: Rafael Borro Gonzalez
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 15/20815-4 - Resolubilidade e hipoeliticidade de operadores diferenciais parciais de primeira ordem e o problema de Riemann-Hilbert
• Beneficiário: Paulo Leandro Dattori da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Regular