Abstract: This paper studies the existence of singular solutions to the nonlinear parabolic-elliptic system for initial data in Lorentz space L^n/2,∞ (Rⁿ), n≥3, only by means of the norm of Lorentz space. The regularized solutions are also obtained by virtue of the time weighted Lorentz space. Moreover, the self-similar solutions are also obtained.

Key words: Parabolic-elliptic system, Lorentz space L^n/2,∞ (Rⁿ), Regular and singular solutions