标题： 非光滑相互作用势的梯度流 显示英文标题

标题： Gradient flows for non-smooth interaction potentials

摘要： 我们处理一个非局部相互作用方程，该方程描述了在一般对称成对相互作用势的影响下粒子密度的演化，这种势不一定以卷积形式存在。 我们描述了凸性（或\lambda -凸性）势的情况，可能在多个点上不光滑，推广了[CDFLS]的结果。 我们还确定了动态仍由连续性方程支配的情况，并且具有特征明确的非局部速度场。 参考文献：[CDFLS] J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, D. Slepcev, 全时间弱测度解和非局部相互作用方程的有限时间聚集，杜克数学杂志 156 (2011), 229--271. 显示英文摘要

摘要： We deal with a nonlocal interaction equation describing the evolution of a particle density under the effect of a general symmetric pairwise interaction potential, not necessarily in convolution form. We describe the case of a convex (or \lambda-convex) potential, possibly not smooth at several points, generalizing the results of [CDFLS]. We also identify the cases in which the dynamic is still governed by the continuity equation with well-characterized nonlocal velocity field. Reference: [CDFLS] J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, D. Slepcev, Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations, Duke Math. J. 156 (2011), 229--271.