论文标题
在$ l^1 \ times w^{1,2} $中的初始数据的立即平滑和全局解决方案中的Keller-Segel系统中，具有逻辑术语在2D中
Immediate smoothing and global solutions for initial data in $L^1\times W^{1,2}$ in a Keller-Segel system with logistic terms in 2D
论文作者
论文摘要
本文讨论了逻辑凯勒 - 塞格模型\ [ 开始{case} u_t =ΔU -χ\ nabla \ cdot（u \ nabla v） +κU-μU^2，\\ \ \ \\ v_t =ΔV -v + u \ end {case} \] 在有界的二维域（具有均匀的Neumann边界条件和参数$χ，κ\ in \ Mathbb {r} $和$μ> 0 $）中，并表明任何非止境初始数据$（u_0，v_0，v_0）\ in L^1 \ in l^1 \ times w^{1,2} $ songe to Plooke in $ \barΩ\ times（0，\ infty）$。
This article deals with the logistic Keller-Segel model \[ \begin{cases} u_t = Δu - χ\nabla\cdot(u\nabla v) + κu - μu^2, \\ \\ v_t = Δv - v + u \end{cases} \] in bounded two-dimensional domains (with homogeneous Neumann boundary conditions and for parameters $χ, κ\in \mathbb{R}$ and $μ>0$), and shows that any nonnegative initial data $(u_0,v_0)\in L^1\times W^{1,2}$ lead to global solutions that are smooth in $\barΩ\times(0,\infty)$.
