On the coercivity of continuously differentiable vector fields

Abstract

Given an arbitrary fixed continuously differentiable vector field on ${\mathbb{R}}^n$, we prove that this vector field is coercive if and only if its conservative part is coercive. We apply this result in order to provide sufficient conditions to guarantee the co-existence of equilibrium states of a continuously differentiable vector field and its conservative part.

4 pages

References in corpus (1)

• A global geometric decomposition of vector fields and applications to topological conjugacy

Cited by in corpus (2)

• The cutoff phenomenon in Wasserstein distance for nonlinear stable Langevin systems with small Lévy noise
• The cutoff phenomenon in total variation for nonlinear Langevin systems with small layered stable noise