A Keller‐Segel‐fluid system with singular sensitivity: Generalized solutions. (19th March 2019)

• Record Type: Journal Article
• Authors: Black, Tobias; Lankeit, Johannes; Mizukami, Masaaki
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 9(2019)
• Page Start: 3002
• Page End: 3020
• Publication Date: 2019-03-19
• Subjects: chemotaxis‐fluid -- global existence -- Keller‐Segel system -- singular sensitivity -- Stokes equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5561
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In bounded smooth domains Ω ⊂ R N, N ∈ {2, 3}, we consider the Keller‐Segel‐Stokes system n t + u · ∇ n = Δ n − χ ∇ · n c ∇ c, c t + u · ∇ c = Δ c − c + n, u t = Δ u + ∇ P + n ∇ ϕ, ∇ · u = 0, and prove global existence of generalized solutions if χ < ∞, N = 2, 5 3, N = 3 . These solutions are such that blow‐up into a persistent Dirac‐type singularity is excluded.