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• #### Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$ ﻿

(2019-11)
We show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has spatial derivative in the John-Nirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ ...