Given that a vector field $X$ is smooth in $\mathbb{R}^2$, what could be an example of an unconservative vector field following said property? I was thinking about $X=(\frac{-y}{x^2+y^2},\frac{x}{x^2+y^2})$, however I don't think it is considered as a smooth vector field as it is undefined at $(0,0)$. Are there any examples of that?
2026-04-09 11:13:53.1775733233
What could be an example of a Vector Field that is smooth but unconservative?
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