Existence and Gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces
The authors study a system of partial differential equations of parabolic type with nonlinearity, describing chemotaxis phenomena. The unknown functions of the system \(u\), \(v\) and \(w\) represent the densities of two interacting populations and, respectively, the concentration of the common chemical attractant. The authors present very precise results of local and global existence in the frame of Besov spaces. Moreover, they prove analytic regularity with respect to the spatial variables. Basic tools in the proofs are dyadic decompositions, paraproduct techniques and Gevrey estimates as in [\textit{C. Foias} and \textit{R. Temam}, J. Funct. Anal. 87, No. 2, 359--369 (1989; Zbl 0702.35203)], see also \textit{H. A. Biagioni} and \textit{T. Gramchev} [J. Differ. Equations 194, No. 1, 140--165 (2003; Zbl 1160.35311)].
scientific article; zbMATH DE number 6848018
scientific article