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Asymptotics of Chemotaxis Systems with Fractional Dissipation for Small Data in Critical Sobolev Space

  • Jaewook AhnEmail author
  • Jihoon Lee
Article
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Abstract

A chemotaxis system with Newtonian attraction and fractional dissipation of order \(\alpha \in (0,2)\) is considered in \({ \mathbb{R} }^{N}\). For initial data belonging to \(L^{1}\cap H^{4}\) but small in \(L^{\frac{N}{ \alpha }}\), \(N=2,3\), 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.

Keywords

Asymptotics Fractional dissipation Kato–Ponce inequality 

Mathematics Subject Classification (2010)

35R11 92C17 

Notes

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsChung-Ang UniversitySeoulRepublic of Korea

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