数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1719-1724.doi: 10.1016/S0252-9602(11)60356-1
刘昕|黄文亮*
LIU Xin, HUANG Wen-Liang*
摘要:
In this note, we give a short proof for the DiPerna-Lions flows associated to ODEs following the method of Crippa and De Lellis [3]. More precisely, assume that [divb]− ∈L∞ loc(Rd), |b|/(1 + |x| log |x|) ∈L∞(Rd) and |∇b| ·(|∇b|) ∈L∞ loc(Rd), where (r) = log ··· log(r + c), c > 0. Then, there exists a unique regular Lagrangian flow associated with the ODE ˙X (t, x) = b(X(t, x)), X(0, x) = x.
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