论文标题
牛顿的排斥和径向限制：融合稳定状态
Newtonian repulsion and radial confinement: convergence towards steady state
论文作者
论文摘要
我们研究了由牛顿排斥驱动的多维聚合方程的较大时间行为，并通过径向吸引力和限制来平衡。如果牛顿排斥对径向限制，我们量化了代数收敛衰减速率朝着独特的稳态。为此，我们使用与正确选择的径向稳态的比较，确定了一个径向稳态的一个参数家族，并证明能量和2-wassertein距离的尺寸依赖性衰减率。我们还研究牛顿的排斥和径向吸引力。当吸引力势为二次时，已知与二次限制一致。在这里，我们研究了radial骨二次吸引力的案例，证明它仍然导致独特的稳态家族。预计该家族将用于相应的比较论点，该论点会产生代数收敛到稳定的令人反感的吸引性溶液。
We investigate the large time behavior of multi-dimensional aggregation equations driven by Newtonian repulsion, and balanced by radial attraction and confinement. In case of Newton repulsion with radial confinement we quantify the algebraic convergence decay rate towards the unique steady state. To this end, we identify a one-parameter family of radial steady states, and prove dimension-dependent decay rate in energy and 2-Wassertein distance, using a comparison with properly selected radial steady states. We also study Newtonian repulsion and radial attraction. When the attraction potential is quadratic it is known to coincide with quadratic confinement. Here we study the case of perturbed radial quadratic attraction, proving that it still leads to one-parameter family of unique steady states. It is expected that this family to serve for a corresponding comparison argument which yields algebraic convergence towards steady repulsive-attractive solutions.
