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Bianchini Stefano, SISSA, ITALY, Properties of mixing BV vector fields
April 6, 2022 | 3:00 pm - 4:00 pm EDT
We consider the density properties of divergence-free vector fields b in L^1([0,1],BV([0,1]^2)) whic
– The map T associating b with its RLF X_t can be extended as a continuous function to the G-set U;
– ergodic and weakly mixing vector fields b are a residual G-set in U;
– strongly mixing vector fields b are a first category set in U;
– exponentially (fast) mixing vector fields are a dense subset of U.
The proof of these results is based on the density of BV vector fields such that X_{t=1} is a permutation of subsquares, and suitable perturbations of this flow to achieve the desired ergodic/mixing behavior. These approximation results have an interest of their own. A discussion on the extension of these results to d >2 is also presented.
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