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Well-posedness and large deviations for the obstacle problem of first-order stochastic conservation laws
Ruoyang Liu, Rangrang Zhang
The paper investigates obstacle problems for first-order stochastic scalar conservation laws, establishing existence and uniqueness of kinetic solutions and proving a Freidlin–Went…
Well-posedness of Dean-Kawasaki Equation with Singular Interactions
Likun Wang, Zhengyan Wu, Rangrang Zhang
Inspired by [Fehrman, Gess; Invent. Math., 2023] and [Fehrman, Gess; Arch. Ration. Mech. Anal., 2024], we consider the Dean-Kawasaki equation with singular interactions and correla…
Well-posedness of the obstacle problem for generalized Dean-Kawasaki equation
Ruoyang Liu, Rangrang Zhang
We investigate the obstacle problem for generalized Dean--Kawasaki equations driven by correlated conservative noise, establishing the existence, uniqueness, and -stability of…
Large deviation principles for the stationary solutions and invariant measures of a class of SPDE with locally monotone coefficients
Yong Liu, Bin Tang, Rangrang Zhang
We establish the well-posedness of stationary solutions for a class of SPDEs with locally monotone coefficients, and prove the Freidlin--Wentzell large deviation principle (LDP) fo…