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

Jaewook Ahn, Jihoon Lee

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)199-215
Number of pages17
JournalActa Applicandae Mathematicae
Volume169
Issue number1
DOIs
StatePublished - 1 Oct 2020

Keywords

  • Asymptotics
  • Fractional dissipation
  • Kato–Ponce inequality

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