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Asymptotics of Chemotaxis Systems with Fractional Dissipation for Small Data in Critical Sobolev Space
- Authors
- Ahn, Jaewook; Lee, Jihoon
- Issue Date
- Oct-2020
- Publisher
- SPRINGER
- Keywords
- Asymptotics; Fractional dissipation; Kato-Ponce inequality
- Citation
- ACTA APPLICANDAE MATHEMATICAE, v.169, no.1, pp 199 - 215
- Pages
- 17
- Journal Title
- ACTA APPLICANDAE MATHEMATICAE
- Volume
- 169
- Number
- 1
- Start Page
- 199
- End Page
- 215
- ISSN
- 0167-8019
1572-9036
- Abstract
- A chemotaxis system with Newtonian attraction and fractional dissipation of order alpha is an element of (0, 2) is considered in R-N. For initial data belonging to L-1 boolean AND H-4 but small in L-N/alpha, 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.
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