arXiv subjects

Wagner A. A. de Moraes

Publications and source records attributed to Wagner A. A. de Moraes.

3 recordsLinked to original sources

arXiv2025

Global hypoellipticity for a class of complex-valued evolution equations on compact Lie groups

We present necessary and sufficient conditions to have global hypoellipticity for a class of complex-valued coefficient first order evolution equations defined on $\mathbb{T}^1 \times G$, where $G$ is a compact Lie group. First, we show that the global hypoellipticity of the constant coefficient operator related to this operator is a necessary condition, but not a sufficient condition. Under certain hypothesis, we show that the global hypoellipticity of this class of operator is completely characterized by Nirenberg-Treves' condition $(\mathcal{P})$.

math.AP↗

arXiv2025

On the Sobolev boundedness of vector fields on compact Riemannian manifolds

We analyze the sharpness of the Sobolev order for left-invariant vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and microlocal analysis, we investigate the asymptotic behavior of eigenvalues associated with these vector fields. As an application, we demonstrate the ill-posedness of a class of Cauchy problems involving left-invariant vector fields on compact Lie groups.

math.AP↗

arXiv2023

Heat and wave type equations with non-local operators, I. Compact Lie groups

We prove existence, uniqueness and give the analytical solution of heat and wave type equations on a compact Lie group $G$ by using a non-local (in time) differential operator and a positive left invariant operator (maybe unbounded) acting on the group. For heat type equations, solutions are given in $L^q(G)$ for data in $L^p(G)$ with $1<p\leqslant 2\leqslant q<+\infty$. We also provide some asymptotic estimates (large-time behavior) for the solutions. Some examples are given. Also, for wave type equations, we give the solution on some suitable Sobolev spaces over $L^2(G)$. We complement our results, by studying a multi-term heat type equation as well.

math.AP↗