Near any blow-up point in the planar Keller-Segel system, the localized L log L norm of u satisfies limsup (1/ln(T/(T-t))) * integral >= delta_0 > 0 as t approaches the blow-up time T.
SIAM Journal on Mathematical Analysis 52 , 2041-2080 (2020)
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Refined temporal asymptotics near blow-up points in the planar Keller-Segel system
Near any blow-up point in the planar Keller-Segel system, the localized L log L norm of u satisfies limsup (1/ln(T/(T-t))) * integral >= delta_0 > 0 as t approaches the blow-up time T.