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

Renjin Jiang, Kangwei Li, Jie Xiao

We show that, if $b\in L^1(0,T;L_{\mathrm{loc}}^1(\mathbb{R}))$ has spatial derivative in the John-Nirenberg space $\mathrm{BMO}(\mathbb{R})$, then it generalizes a unique flow $ϕ(…