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

Kyungkeun Kang, Kyunghwa Kim, Changwook Yoon

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1 Citation (Scopus)

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

Bibliographical note

Funding Information:
Authors greatly appreciate valuable comments and suggestions of the anonymous reviewer of this paper. Kyungkeun Kang's work is partially supported by National Research Foundation of Korea (NRF) grants funded by the Korea government (MSIP) (NRF-2017R1A2B4006484 and NRF-2015R1A5A1009350). Changwook Yoon was supported by National Research Foundation of Korea (NRF) grants funded by the Korea government (MSIP) (NRF-2017R1D1A1B03031035 and NRF-2017R1E1A1A03070652).

Publisher Copyright:
© 2019 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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