Dean-Kawasaki equation with initial condition in the space of positive distributionsMI 03.04.011 (Boltzmannstr. 3, 85748 Garching)

Motivated from statistical physics, the Dean-Kawasaki Equation aims to describe the density of a system of fluctuating particles. However, it was shown by Konarovskyi, Lehmann and von Renesse that in the space of probability measures the equation only admits solutions given by empirical measures. But what happens if we allow solutions and initial conditions with infinite mass, e.g. starting from the Lebesgue measure? In this talk we will show that even allowing infinite mass, the Dean-Kawasaki equation only admits solutions if its initial condition is a suitable multiple of an empirical measure. Joint work with Vitalii Konarovskyi, arXiv 2311.10006.