3 years ago

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

Adalberto P. Bergamasco, Paulo L. Dattori Da Silva, Rafael B. Gonzalez

Publication date: October 2018

Source: Bulletin des Sciences Mathématiques, Volume 148

Author(s): Adalberto P. Bergamasco, Paulo L. Dattori da Silva, Rafael B. Gonzalez

Abstract

This work deals with global solvability of a class of vector fields of the form L=/t+(a(x)+ib(x))(/x+λ/y), where a,bC(T1,R) and λR, defined on the three-dimensional torus T3(x,y,t)R3/2πZ3. 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.

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