5 papers
Convergence to the Dynamical Model under a Vanishing Quintic Perturbation I: A Paracontrolled Approach
Zikai Chen, Seiichiro Kusuoka
We study local convergence to the dynamical model under a vanishing quintic perturbation. More precisely, on the three-dimensional torus we consider $$\partial_tu_\varepsil…
Kinetic Fokker--Planck Equations with Drifts in a Supercritical Range
Zikai Chen, Chongyang Ren
We investigate kinetic Fokker--Planck equations with rough divergence-free drifts in anisotropic mixed Lebesgue spaces. The divergence-free structure yields an energy cancellation…
Well-Posedness for SDEs with Logarithmical Critical Distributional Drifts
Zikai Chen, Zimo Hao, Xicheng Zhang
We study the stochastic differential equation on , where is a time-dependent, divergence-free distributional drift of critical…
Kinetic SDEs with subcritical distributional drifts
Zikai Chen, Zimo Hao, Xicheng Zhang
In this paper we study the well-posedness of the kinetic stochastic differential equation (SDE) in driven by Brownian motion: $$\mathord{\rm d} X_t=V_t\mat…
On one typical Einstein-Weyl equation: inverse spectral transform for theCauchy problem, longtime behaviour of the solutions and implicit solutions
Ge Yi, Zikai Chen, Kelei Tian +1
In this paper, we study one typical Einstein-Weyl equation. It arises from Ferapontov and Kruglikov's investigation on the integrability of several dispersionless partial different…