TY - JOUR
T1 - Asymptotics of Chemotaxis Systems with Fractional Dissipation for Small Data in Critical Sobolev Space
AU - Ahn, Jaewook
AU - Lee, Jihoon
N1 - Publisher Copyright:
© 2019, Springer Nature B.V.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - A chemotaxis system with Newtonian attraction and fractional dissipation of order α∈ (0 , 2 ) is considered in RN. For initial data belonging to L1∩ H4 but small in LNα, N= 2 , 3 , the temporal decay and the asymptotic behavior of a global classical solution are established. In particular, we derive a precise decay estimate for higher Sobolev norms.
AB - A chemotaxis system with Newtonian attraction and fractional dissipation of order α∈ (0 , 2 ) is considered in RN. For initial data belonging to L1∩ H4 but small in LNα, N= 2 , 3 , the temporal decay and the asymptotic behavior of a global classical solution are established. In particular, we derive a precise decay estimate for higher Sobolev norms.
KW - Asymptotics
KW - Fractional dissipation
KW - Kato–Ponce inequality
UR - http://www.scopus.com/inward/record.url?scp=85074817350&partnerID=8YFLogxK
U2 - 10.1007/s10440-019-00296-8
DO - 10.1007/s10440-019-00296-8
M3 - Article
AN - SCOPUS:85074817350
SN - 0167-8019
VL - 169
SP - 199
EP - 215
JO - Acta Applicandae Mathematicae
JF - Acta Applicandae Mathematicae
IS - 1
ER -