5 papers
The stochastic Keller--Segel system in critical spaces
Jae-Hwan Choi, Ankit Kumar, Andrea Pitrone +2
We study stochastic, parabolic-parabolic Keller--Segel equations on the -dimensional torus in scaling critical Besov spaces, for . Using stochastic maximal regularity…
Ergodicity for the Dean--Kawasaki Equation with Dirichlet Boundary Conditions: Taming the Square-Root
Shyam Popat, Zhengyan Wu
In this paper, we establish the ergodicity of generalized Dean--Kawasaki equations with correlated noise and Dirichlet boundary conditions. In contrast to the ergodicity results of…
Small noise fluctuations and large deviations of conservative SPDEs with Dirichlet boundary conditions
Shyam Popat
We establish a central limit theorem and large deviations principle that characterises small noise fluctuations of the generalised Dean--Kawasaki stochastic PDE. The fluctuations a…
Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions
Lukas Gräfner, Nicolas Perkowski, Shyam Popat
In this paper we extend the theory of energy solutions for singular SPDEs, focusing on equations driven by highly irregular noise with bilinear nonlinearities, including scaling cr…
Well-Posedness of the generalised Dean-Kawasaki Equation with correlated noise on bounded domains
Shyam Popat
In this paper, we extend the notion of stochastic kinetic solutions introduced in arXiv:2108.08858 to establish the well-posedness of stochastic kinetic solutions of generalized De…