Blow-up for a Three Dimensional Keller-Segel Model with Consumption of Chemoattractant

Abstract

We investigate blow-up properties for the initial-boundary value problem of a Keller-Segel model with consumption of chemoattractant when the spatial dimension is three. Through a kinetic reformulation of the Keller-Segel model, we first derive some higher-order estimates and obtain certain blow-up criteria for the local classical solutions. These blow-up criteria generalize the results in [4,5] from the whole space ${\mathbb{R}}^3$ to the case of bounded smooth domain $\Omega \subset {\mathbb{R}}^3$. Lower global blow-up estimate on $\Vert n{\Vert }_{L^{\infty }(\Omega )}$ is also obtained based on our higher-order estimates. Moreover, we prove local non-degeneracy for blow-up points.

References in corpus (2)

• Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system
• Global Existence and Asymptotic Behavior of Solutions to a Chemotaxis-Fluid System on General Bounded Domain

Cited by in corpus (4)

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• Low modes regularity criterion for a chemotaxis-Navier-Stokes system
• Boundedness and stabilization in a two-species chemotaxis system with signal absorption
• Application of harmonic analysis techniques to regularity problems of dissipative equations