论文标题
堕落的两个物种和交叉诱使系统中全球存在和爆炸的鲜明条件
Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
论文作者
论文摘要
我们考虑了一个具有两个物种的退化趋化模型，在维度$ d \ geq 3 $中，并找到了两个关键曲线，并在一个点上相交的两个临界曲线，这些曲线将全球存在和薄弱的解决方案炸毁了问题。更确切地说，高于这些曲线（即亚临界情况），该问题接受了通过强大解决方案对近似系统的限制获得的全球弱解决方案。基于解决方案的第二刻，构建初始数据以确保在这些曲线以下（即关键和超临界情况）以下的有限时间内发生爆炸。此外，在临界曲线上讨论了自由能功能最小功能的最小化器的存在或不存在，如果初始数据的大小很小，则在全球范围内存在解决方案。我们还研究了再次给出精致标准的临界线之间的交叉点，以再次给出质量的精致标准，以区分全球存在与爆炸之间的二分法。我们还表明，这两种物种都是同时进行的。
We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension $d\geq 3$ and find two critical curves intersecting at one same point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the problem admits a global weak solution obtained by the limits of strong solutions to an approximated system. Based on the second moment of solutions, initial data are constructed to make sure blow up occurs in finite time below these curves (i.e. critical and supercritical cases). In addition, the existence or non-existence of minimizers of free energy functional is discussed on the critical curves and the solutions exist globally in time if the size of initial data is small. We also investigate the crossing point between the critical lines in which a refined criteria in terms of the masses is given again to distinguish the dichotomy between global existence and blow up. We also show that the blow ups is simultaneous for both species.
