简介:Inthisnote,wegiveashortprooffortheDiPerna-LionsflowsassociatedtoODEsfollowingthemethodofCrippaandDeLellis[3].Moreprecisely,assumethat[divb]∈Ll∞oc(Rd),|b|/(1+|x|log|x|)∈L∞(Rd)and|b|φ(|b|)∈Ll1oc(Rd),whereφ(r)=loglog(r+c),c>0.Then,thereexistsauniqueregularLagrangianflowassociatedwiththeODEX˙(t,x)=b(X(t,x)),X(0,x)=x.