Global solvability and global hypoellipticity for a class of complex vector fields on the 3-torus

摘要

This work deals with global solvability and global hypoellipticity of complex vector fields of the form L = ∂/∂t + ib_1(t)∂/∂x_1 + ib_2(t)∂/∂x_2, defined on T~3 ≃ R~3/2πZ~3, where both b_1 and b_2 belong to C~∞(T~1; R). The solvability and hypoellipticity depend on condition (P) and also on Diophantine properties of the coefficients.