an:05492830
Zbl 1173.35406
da Silva, Paulo L. Dattori
Nonexistence of global solutions for a class of complex vector fields on two-torus
EN
J. Math. Anal. Appl. 351, No. 2, 543-555 (2009).
00243987
2009
j
35F10 35A21
global solvability; solvability near the characteristic set; complex vector fields; condition (\(\mathcal P\)); Sussmann orbits; propagation of singularities; bicharacteristics
Summary: The goal of this paper is study the global solvability of a class of complex vector fields of the special form L \(= \partial / \partial t + (a+ib)(x)\partial / \partial x , a,b \in C^\infty (S^1; \mathbb R)\), defined on two-torus \(\mathbb T^2 \cong \mathbb R^2 / 2\pi \mathbb Z^2\). The kernel of transpose operator \(^t\)L is described and the solvability near the characteristic set is also studied.