Spatial Analyticity of Solutions to Keller-Segel Equation of Parabolic-Elliptic Type

In this article, spatial analyticity of solutions to Keller-Segel equation of parabolic-elliptic type with generalized dissipation is presented. First, we prove the analyticity of local solutions to system with large rough initial data in Modulation spaces with . Secondly, we establish the analyticity of solutions to the system with initial data in critical Fourier-Besov spaces with (or ) and , the main method is so-called Gevrey estimates, which is motivated by the works of Foias and Temam (Foias in Contemp Math 208:151-180, 1997). In the critical case that , we prove global Gevrey analyticity for small initial data in critical Fourier-Besov spaces with and . The results of us particularly imply temporal decay rates of higher Fourier-Besov norms of solutions.