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math.AP2019★ 23 cited
Generalized solutions for a system of partial differential equations arising from urban crime modeling with a logistic source term
Frederic Heihoff
We consider the system \[ \left\{ \begin{aligned} u_t &= Δu - χ\nabla \cdot ( \tfrac{u}{v} \nabla v) - uv + ρu - μu^2, \\ v_t &= Δv - v + u v \end{aligned} \right. \tag{} \]…
math.AP2019★ 8 cited
Global mass-preserving solutions for a two-dimensional chemotaxis system with rotational flux components coupled with a full Navier-Stokes equation
Frederic Heihoff
We study the chemotaxis-Navier-Stokes system \[\left\{\; \begin{aligned} n_t + u\cdot\nabla n &=Δn - \nabla\cdot (nS(x,n,c)\nabla c), &&x\inΩ, t > 0, \\ c_t + u\cdot\nabla c &=Δc -…