Well‐posedness and asymptotic behavior for the fractional Keller–Segel system in critical Besov–Herz‐type spaces

One of the most important models for understanding chemotactic aggregation is the Keller–Segel system. We analyze the time‐fractional Keller–Segel system in a new framework; we derive the global well‐posedness and the asymptotic behavior of solutions in critical Besov‐weak‐Herz spaces that consist in Besov spaces based on weak‐Herz spaces.