Ill-posedness of the pure-noise Dean-Kawasaki equation

Lorenzo Dello Schiavo, Vitalii Konarovskyi

We prove that the Dean-Kawasaki-type stochastic partial differential equation $$\partial \rho =\nabla \cdot (\sqrt{\rho }\xi )+\nabla \cdot \left(\rho H(\rho )\right)$$ with vector-valued sp…