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- W2007066174 abstract "We shall show existence of global strong solution to the semi-linear Keller–Segel system in Rn, n⩾3, of parabolic–parabolic type with small initial data u0∈Hnr−2,r(Rn) and v0∈Hnr,r(Rn) for max{1,n/4}<r<n/2. Our method is based on the perturbation of linealization together with the Lp–Lq estimates of the heat semigroup and the fractional powers of the Laplace operator. As a by-product of our method, we shall prove the decay property of solutions as the time goes to infinity." @default.
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- W2007066174 date "2009-07-01" @default.
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- W2007066174 title "Global strong solution to the semi-linear Keller–Segel system of parabolic–parabolic type with small data in scale invariant spaces" @default.
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- W2007066174 doi "https://doi.org/10.1016/j.jde.2009.03.027" @default.
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