Existence of probabilistically weak renormalized kinetic solutions and a restricted large deviation principle are established for the Dean-Kawasaki equation with Biot-Savart and Keller-Segel singular kernels via regularization and a new exponential tightness argument.
Conservative stochastic PDE and fluctuations of the sym- metric simple exclusion process.Communications in Mathematical Physics, 407:Paper No
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Dean-Kawasaki Equation with Biot-Savart and Keller-Segel Interactions: Existence and Large Deviations
Existence of probabilistically weak renormalized kinetic solutions and a restricted large deviation principle are established for the Dean-Kawasaki equation with Biot-Savart and Keller-Segel singular kernels via regularization and a new exponential tightness argument.