Existence of intermediate weak solution to the equations of multi-dimensional chemotaxis systems

Research output: Contribution to journalArticle

Abstract

We prove the global-in-time existence of intermediate weak solutions of the equations of chemotaxis system in a bounded domain of R² or R³ with initial chemical concentration small in H¹. No smallness assumption is imposed on the initial cell density which is in L². We first show that when the initial chemical concentration c₀ is small only in H¹ and (n₀−n∞,c₀) is smooth, the classical solution exists for all time. Then we construct weak solutions as limits of smooth solutions corresponding to mollified initial data. Finally we determine the asymptotic behavior of the global solutions. Copyright © 2015 Southwest Missouri State University.
Original languageEnglish
Pages (from-to)861-875
JournalDiscrete and Continuous Dynamical Systems
Volume36
Issue number2
DOIs
Publication statusPublished - 2016

Fingerprint

Chemotaxis
Weak Solution
Smooth Solution
Classical Solution
Global Solution
Bounded Domain
Asymptotic Behavior
Cell

Citation

Li, T., & Suen, A. (2016). Existence of intermediate weak solution to the equations of multi-dimensional chemotaxis systems. Discrete and Continuous Dynamical Systems, 36(2), 861-875.

Keywords

  • Asymptotic behavior
  • Chemotaxis
  • Energy estimates
  • Global existence
  • Intermediate weak solution
  • Keller-Segel model