ArticleStochastic partial differential equations : analysis and computations2025
An additive-noise approximation to Keller-Segel-Dean-Kawasaki dynamics: local well-posedness of paracontrolled solutions.
Article in Stochastic partial differential equations : analysis and computations, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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- An additive-noise approximation to Keller-Segel-Dean-Kawasaki dynamics: local well-posedness of paracontrolled solutions.Stochastic partial differential equations : analysis and computations · 2025Article
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Abstract
Using the method of paracontrolled distributions, we show the local well-posedness of an additive-noise approximation to the fluctuating hydrodynamics of the Keller-Segel model on the two-dimensional torus. Our approximation is a non-linear, non-local, parabolic-elliptic stochastic PDE with an irregular, heterogeneous space-time noise. As a consequence of the irregularity and heterogeneity, solutions to this equation must be renormalised by a sequence of diverging fields. Using the symmetry of the elliptic Green's function, which appears in our non-local term, we establish that the renormalisation diverges at most logarithmically, an improvement over the linear divergence one would expect by power counting. Similar cancellations also serve to reduce the number of diverging counterterms.
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