Existence of weak and regular solutions for Keller–Segel system with degradation coupled to fluid equations

Kyungkeun Kang, Kyunghwa Kim, Changwook Yoon

Research output: Contribution to journalArticle

Abstract

We establish the global well-posedness for the following chemotaxis-fluid system {∂tn+u⋅∇n=Δn−∇⋅(n∇c)−μnq,∂tc+u⋅∇c=Δc−c+n,∂tu+κ(u⋅∇)u+∇P=Δu−n∇ϕ,∇⋅u=0, in Rd, d=2,3, where μ>0, q>2− [Formula presented] and κ∈{0,1}. For either q≥2, (κ,d)=(1,2) or q>2, (κ,d)=(0,3), we prove the global existence of regular solutions. In case that q>2− [Formula presented] and κ=0, very weak solutions are constructed as well.

Original languageEnglish
Article number123750
JournalJournal of Mathematical Analysis and Applications
Volume485
Issue number1
DOIs
Publication statusPublished - 2020 May 1

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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