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

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 نشر من قبل Renjin Jiang
 تاريخ النشر 2018
  مجال البحث
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We show that, if $bin L^1(0,T;L^1_{mathrm{loc}}(mathbb{R}))$ has spatial derivative in the John-Nirenberg space $mathrm{BMO}(mathbb{R})$, then it generalizes a unique flow $phi(t,cdot)$ which has an $A_infty(mathbb R)$ density for each time $tin [0,T]$. Our condition on the map $b$ is optimal and we also get a sharp quantitative estimate for the density. As a natural application we establish a well-posedness for the Cauchy problem of the transport equation in $mathrm{BMO}(mathbb R)$.



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