Well-posedness of the Dean--Kawasaki and the nonlinear Dawson--Watanabe equation with correlated noise

Benjamin Fehrman; Benjamin Gess

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Well-posedness of the Dean--Kawasaki and the nonlinear Dawson--Watanabe equation with correlated noise

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arxiv 2108.08858 v3 pith:CRUW5CU3 submitted 2021-08-19 math.PR math.AP

Benjamin Fehrman , Benjamin Gess This is my paper · ORCID

classification math.PRmath.AP

keywords equationdean--kawasakinoisewell-posednesscorrelateddawson--watanabeincludingnonlinear

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In this paper we prove the well-posedness of the generalized Dean--Kawasaki equation driven by noise that is white in time and colored in space. The results treat diffusion coefficients that are only locally 1/2-H\"older continuous, including the square root. This solves several open problems, including the well-posedness of the Dean--Kawasaki equation and the nonlinear Dawson--Watanabe equation with correlated noise.

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