论文标题
强烈的排斥能够在排斥趋化趋化系统中导致平滑溶液，即使从高度不规则的初始数据开始？
Does strong repulsion lead to smooth solutions in a repulsion-attraction chemotaxis system even when starting with highly irregular initial data?
论文作者
论文摘要
已经有很好的确定，在“吸引力”中，形式的keller-segel系统\ begin {equation*} \左边\{ \ begin {Aligned} u_t＆=Δu -χ\ nabla \ cdot（u \ nabla v） +ξ\ nabla \ cdot（u \ nabla w），\\ τv_t＆=ΔV +αu -βv，\\ τw_t＆=ΔW +γu-ΔW \ end {Aligned} \正确的。 \ end {equation*}在平稳的界面$ω\ subseteq \ mathbb {r}^n $，$ n \ in \ mathbb {n} $中，带有neumann边界条件和参数条件$χ，ξ\ geq 0 $，geq 0 $，$α，$α，$α，β，β，β，γ> 0 $ and $ unite unite unite unite，如果排斥性趋化性比其有吸引力的对应物更强大，则可以在许多情况下排除爆炸。 In this paper, we will go - in a sense - a step further than this by studying the same system with initial data that could already be understood as being in a blown-up state (e.g. a positive Radon measure for the first solution component) and then ask the question whether sufficiently strong repulsion has enough of a regularizing effect to lead to the existence of a smooth solution, which is still connected to said initial data in a sensible fashion.关于这一点，我们实际上确定在二维抛物线 - 抛物线系统和二维和三维抛物线纤维纤维化系统中，在适当假设下对排斥和吸引力的相互作用以及初始数据的构建可能是可能的。
It has been well established that, in attraction-repulsion Keller-Segel systems of the form\begin{equation*} \left\{ \begin{aligned} u_t &= Δu - χ\nabla \cdot (u\nabla v) + ξ\nabla \cdot (u\nabla w), \\ τv_t &= Δv + αu - βv,\\ τw_t &= Δw + γu - δw \end{aligned} \right. \end{equation*} in a smooth bounded domain $Ω\subseteq \mathbb{R}^n$, $n\in\mathbb{N}$, with Neumann boundary conditions and parameters $χ, ξ\geq 0$, $α,β,γ,δ> 0$ and $τ\in \{0,1\}$, finite-time blow-up can be ruled out in many scenarios given sufficiently smooth initial data if the repulsive chemotaxis is sufficiently stronger than its attractive counterpart. In this paper, we will go - in a sense - a step further than this by studying the same system with initial data that could already be understood as being in a blown-up state (e.g. a positive Radon measure for the first solution component) and then ask the question whether sufficiently strong repulsion has enough of a regularizing effect to lead to the existence of a smooth solution, which is still connected to said initial data in a sensible fashion. Regarding this, we in fact establish that the construction of such a solution is possible in the two-dimensional parabolic-parabolic system and the two- and three-dimensional parabolic-elliptic system under appropriate assumptions on the interaction of repulsion and attraction as well as the initial data.
