Over the past two decades, gradient flows in the optimal transport framework have received significant attention due to their wide-ranging applications. However, a general theory for non-convex energy functionals remains largely open. In my poster, I will discuss the theory of asymptotic convergence of the McKean-Vlasov equation
\begin{align}
\partial_t \mu_t = \operatorname{div} \left( \nabla \mu_t + \mu_t \nabla \left[ V + W \ast \mu_t \right] \right)
\end{align}
for non-convex functionals associated with $V, W$ on $\mathcal{P}_2(\mathbb{T}^n)$, by applying \{L}ojasiewicz-Simon theory in its tangent space. As a fundamental application, I will present the asymptotic behaviour of parabolic--elliptic Keller--Segel system
\begin{align}
\begin{cases}
\partial_t \rho
= \nabla\!\cdot\!\big(\nabla \rho - \chi\, \rho\, \nabla c\big)
+ \nabla\!\cdot\!\big(\rho\,\nabla V\big),\\[0.2em]
(-\Delta + \alpha)\,c \;=\; \rho - \overline{\rho}, \qquad \alpha\ge 0.
\end{cases}
\end{align}