Renormalized solutions to a chemotaxis system with consumption of chemoattractant
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This article concerns the high-dimensional chemotaxis system with consumption of chemoattractant
ut = ∆u - ∇ ∙ (u∇v),
vt = ∆v - uv,
under homogeneous boundary conditions of Neumann type, in a bounded domain Ω ⊂ ℝn (n ≥ 4) with smooth boundary. We prove that if the initial data satisfy u0 ∈ C0(Ω̅) and v0 ∈ W1,q(Ω) for some q > n, this model possesses at least one global renormalized solution.
CitationWang, H., & Li, Y. (2019). Renormalized solutions to a chemotaxis system with consumption of chemoattractant. Electronic Journal of Differential Equations, 2019(38), pp. 1-19.
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