Study on a chemotaxis equation in the two-dimensional whole space

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We considered a simplified Keller-Segel equation(parabolic-elliptic system) in the two-dimensional whole space, which is a mathematical model of chemotaxis, and studied the global existence, uniqueness, boundedness and large-time behavior of nonnegative solutions to the Cauchy problem of the equation. We first established the local existence in time, uniqueness and regularity of mild solutions. In the subcritical case, we showed the global existence in time and decay estimates of nonnegative mild solutions without decay conditions of initial data, and then the convergence to a forward self-similar solution and convergence rates.