Skip to main content
MathOverflow

Return to Question

Missing $$
Source Link
LSpice
LSpice
  • 12.9k
  • 4
  • 45
  • 69

If $M$ is a compact Riemannian manifold, is the space of $C^{\infty}$ divergence free-free vector fields dense in the space of $C^r$ divergence free-free vector fields, in the $C^r$ topology (r\geq 1$r\geq 1$)? How about if we consider divergence free-free vector fields compactly supported on $\mathbb R^n$?

If $M$ is a compact Riemannian manifold, is the space of $C^{\infty}$ divergence free vector fields dense in the space of $C^r$ divergence free vector fields, in the $C^r$ topology (r\geq 1)? How about if we consider divergence free vector fields compactly supported $\mathbb R^n$?

If $M$ is a compact Riemannian manifold, is the space of $C^{\infty}$ divergence-free vector fields dense in the space of $C^r$ divergence-free vector fields, in the $C^r$ topology ($r\geq 1$)? How about if we consider divergence-free vector fields compactly supported on $\mathbb R^n$?

Source Link
Radu
Radu
  • 19
  • 1

Can divergence free vector fields be approximated by smooth ones?

If $M$ is a compact Riemannian manifold, is the space of $C^{\infty}$ divergence free vector fields dense in the space of $C^r$ divergence free vector fields, in the $C^r$ topology (r\geq 1)? How about if we consider divergence free vector fields compactly supported $\mathbb R^n$?