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

Jaewook Ahn; Jihoon Lee

doi:10.1007/s10440-019-00296-8

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

Jaewook Ahn
, Jihoon Lee

Department of Mathematics

Chung-Ang University

Research output: Contribution to journal › Article › peer-review

Abstract

A chemotaxis system with Newtonian attraction and fractional dissipation of order α∈ (0 , 2 ) is considered in R^N. 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 language	English
Pages (from-to)	199-215
Number of pages	17
Journal	Acta Applicandae Mathematicae
Volume	169
Issue number	1
DOIs	https://doi.org/10.1007/s10440-019-00296-8
State	Published - 1 Oct 2020

Keywords

Asymptotics
Fractional dissipation
Kato–Ponce inequality

Access to Document

10.1007/s10440-019-00296-8

Cite this

@article{669a4720d757476b9f53c1d434bfbdfb,

title = "Asymptotics of Chemotaxis Systems with Fractional Dissipation for Small Data in Critical Sobolev Space",

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.",

keywords = "Asymptotics, Fractional dissipation, Kato–Ponce inequality",

author = "Jaewook Ahn and Jihoon Lee",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature B.V.",

year = "2020",

month = oct,

day = "1",

doi = "10.1007/s10440-019-00296-8",

language = "English",

volume = "169",

pages = "199--215",

journal = "Acta Applicandae Mathematicae",

issn = "0167-8019",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Asymptotics of Chemotaxis Systems with Fractional Dissipation for Small Data in Critical Sobolev Space

AU - Ahn, Jaewook

AU - Lee, Jihoon

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 - https://www.scopus.com/pages/publications/85074817350

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 -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this