TY - JOUR
T1 - End-point maximal regularity and its application to two-dimensional Keller-Segel system
AU - Ogawa, Takayoshi
AU - Shimizu, Senjo
PY - 2010/1
Y1 - 2010/1
N2 - We prove the maximal Lρ regularity of the Cauchy problem of the heat equation in the Besov space Ḃ10,ρ (ℝn) 1 > ρ ≤ ∞, which is not UMD space. And as its application, we establish the time local well-posedness of the solution of two dimensional nonlinear parabolic system with the Poisson equation in Ḃ10,2ℝ2), where the equation is considered in the space invariant by a scaling and particularly the natural free energy is well defined from the initial time. The small data global existence is also obtained in the same class.
AB - We prove the maximal Lρ regularity of the Cauchy problem of the heat equation in the Besov space Ḃ10,ρ (ℝn) 1 > ρ ≤ ∞, which is not UMD space. And as its application, we establish the time local well-posedness of the solution of two dimensional nonlinear parabolic system with the Poisson equation in Ḃ10,2ℝ2), where the equation is considered in the space invariant by a scaling and particularly the natural free energy is well defined from the initial time. The small data global existence is also obtained in the same class.
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U2 - 10.1007/s00209-009-0481-3
DO - 10.1007/s00209-009-0481-3
M3 - Article
AN - SCOPUS:76349090446
SN - 0025-5874
VL - 264
SP - 601
EP - 628
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3
ER -