This paper is devoted to the global existence of weak solutions to the following degenerate kinetic model of chemotaxis (0.1)$\left\{\begin{array}{c}{u}_t=\Delta \left(\gamma \left(v\right)u\right)\hfill \\ \tau v_t=\Delta v-v+u\hfill \end{array}\right.$in a smooth bounded domain with no-flux boundary conditions under the assumption $0\le \tau <{\left(\underset{(0,\infty )}{sup}\gamma \right)}^{-1}$. The problem features a positive signal-dependent motility function $\gamma \left(\cdot \right)$ which may vanish as $v$ becomes unbounded. In this paper, we first modify the comparison approach developed recently in Fujie and Jiang (2020); Fujie and Jiang (2021) to derive the upper bounds of $v$ under the slightly weakened above assumptions on $\gamma \left(\cdot \right)$. Then by introducing a suitable approximation scheme which is compatible with the comparison method, we establish the global existence of weak solutions in any spatial dimension via compactness argument. Our weak solution has higher regularity than those obtained in previous literature (Burger et al., 2020; Desvillettes et al., 2019; Tao and Winkler, 2017).

本文致力于以下趋化性的退化动力学模型（0.1）的弱解的整体存在$\left\{\begin{array}{c}{ü}_{Ť}=\Delta （\gamma （v）ü）\hfill \\ \tau v_{Ť}=\Delta v-v+ü\hfill \end{array}\right.$假设下在无通量边界条件下的光滑有界域中 $0\le \tau <{（\underset{（0，\infty ）}{SUP}\gamma ）}^{-\mathrm{1个}}$。该问题具有正信号依赖的运动功能$\gamma （\cdot ）$ 可能消失为 $v$变得无界。在本文中，我们首先修改了最近在Fujie and Jiang（2020）中开发的比较方法。Fujie and Jiang（2021）推导$v$ 在上述假设略微减弱的情况下 $\gamma （\cdot ）$。然后，通过引入与比较方法兼容的合适的近似方案，我们通过紧致性参数建立了在任何空间维上的弱解的整体存在性。我们的弱解比以前的文献（Burger等，2020; Desvillettes等，2019; Tao和Winkler，2017）具有更高的规律性。