Well-posedness of nonlinear diffusion equations with nonlinear, conservative noise

Abstract

We prove the pathwise well-posedness of stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. As a consequence, the generation of a random dynamical system is obtained. This extends results of the second author and Souganidis, who considered analogous spatially homogeneous and first-order equations, and earlier works of Lions, Perthame, and Souganidis.

57 pages

References in corpus (1)

• A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law

Cited by in corpus (3)

• On Dean-Kawasaki Dynamics with Smooth Drift Potential
• Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process
• Dean-Kawasaki Dynamics: Ill-posedness vs. Triviality