实直线上的可逆聚结-破碎Wasserstein动力学
Reversible Coalescing-Fragmentating Wasserstein Dynamics on the Real Line
摘要：
我们引入了一类具有不同尺寸尺度扩散系数的颗粒的可逆破碎-凝聚过程，这些过程在实线上具有严格的局部相互作用，作为流体胶体运动的数学严格描述。相关的测量值过程提供了一个弱解的修正Dean-Kawasaki方程的过冷液体没有耗散。我们的建设是基于一个全新的家庭的平衡测度的相关动力学和Dirichlet形式的介绍和分析。我们确定的内在度量作为二次Wasserstein距离，这使得该过程的Wasserstein扩散的一个非平凡的例子。
英文摘要：
We introduce a family of reversible fragmentating-coagulating processes of particles of varying size-scaled diffusivity with strictly local interaction on the real line as mathematically rigorous description of colloidal motion of fluids. The associated measure-valued process provides a weak solution to a corrected Dean-Kawasaki equation for supercooled liquids without dissipation. Our construction is based on the introduction and analysis of a fundamentally new family of equilibrium measures for the associated dynamics and their Dirichlet forms. We identify the intrinsic metric as the quadratic Wasserstein distance, which makes the process a non-trivial example of Wasserstein diffusion.
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