Let $M$ be a closed 3-dimensional Riemann manifold and let $3\le r\le \infty$. We prove that there exists an open dense subset in the space of $C^r$ volume-preserving Anosov flows on $M$ such that all the flows in it are exponentially mixing.
"Exponential mixing for generic volume-preserving Anosov flows in dimension three." J. Math. Soc. Japan 70 (2) 757 - 821, April, 2018. https://doi.org/10.2969/jmsj/07027595