Zobrazeno 1 - 10
of 89
pro vyhledávání: '"Rongchan Zhu"'
Publikováno v:
Journal of the European Mathematical Society (EMS Publishing); 2024, Vol. 26 Issue 1, p163-260, 98p
Autor:
Rongchan Zhu, Xiangchan Zhu
Publikováno v:
Potential Analysis. 58:295-330
We prove the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on $\mathbb{R}^3$ to the dynamical $\Phi^4_3$ model by paracontrolled distributions on weighted Besov space. Our approach depends on the delicate
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8302609e5d3c9c30a45c9c7efd549f2f
https://doi.org/10.1007/s11118-021-09941-0
https://doi.org/10.1007/s11118-021-09941-0
We develop a new stochastic analysis approach to the lattice Yang--Mills model at strong coupling in any dimension $d>1$, with t' Hooft scaling $\beta N$ for the inverse coupling strength. We study their Langevin dynamics, ergodicity, functional ineq
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1d0eae008ffca1976068246daa59ccf2
Autor:
Rui Zhang, Peiyan Hu, Qi Meng, Yue Wang, Rongchan Zhu, Bingguang Chen, Zhi-Ming Ma, Tie-Yan Liu
We present the deep random vortex network (DRVN), a novel physics-informed framework for simulating and inferring the fluid dynamics governed by the incompressible Navier-Stokes equations. Unlike the existing physics-informed neural network (PINN), w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8239588ee7cb99ce560e1e51f3122769
https://doi.org/10.1063/5.0110342
https://doi.org/10.1063/5.0110342
Autor:
Rongchan Zhu, Ting Ma
Publikováno v:
Journal of Mathematical Analysis and Applications. 469:623-660
In this paper we present the Wong–Zakai approximation results for a class of nonlinear SPDEs with locally monotone coefficients and driven by multiplicative Wiener noise. This model extends the classical monotone one and includes examples like stoc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f0adcc3826b53ae1ab55a02b0474ccf1
https://doi.org/10.1016/j.jmaa.2018.09.031
https://doi.org/10.1016/j.jmaa.2018.09.031
Publikováno v:
Discrete & Continuous Dynamical Systems - B. 24:4021-4030
In this paper, we prove that the solution constructed in \cite{BR16} satisfies the stochastic vorticity equations with the stochastic integration being understood in the sense of the integration of controlled rough path introduced in \cite{G04}. As a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a97428861f85e588d50f55d4f9f0f28f
https://doi.org/10.3934/dcdsb.2019048
https://doi.org/10.3934/dcdsb.2019048
Autor:
Xiangchan Zhu, Rongchan Zhu
Publikováno v:
Science China Mathematics. 63:381-410
We construct a piecewise linear approximation for the dynamical $$\Phi_3^4$$ model on $$\mathbb{T}^3$$. The approximation is based on the theory of regularity structures developed by Hairer (2014). They proved that renormalization in a dynamical $$\P
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::687c17a0478653d74fb11854e956b488
https://doi.org/10.1007/s11425-017-9269-1
https://doi.org/10.1007/s11425-017-9269-1
In this paper, we investigate both deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev space (H)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::12a3c795e74e620e958e8dd7e6ca68f9
https://pub.uni-bielefeld.de/record/2950201
https://pub.uni-bielefeld.de/record/2950201
We consider the stochastic two-dimensional Cahn-Hilliard equation which is driven by the derivative in space of a space-time white noise. We use two different approaches to study this equation. First we prove that there exists a unique solution Y to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b52a02394d1e47fa9c3a8c5a4a4017d2
https://pub.uni-bielefeld.de/record/2956278
https://pub.uni-bielefeld.de/record/2956278
We establish global-in-time existence and non-uniqueness of probabilistically strong solutions to the three dimensional Navier--Stokes system driven by space-time white noise. In this setting, solutions are expected to have space regularity at most $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::69014b4097b98af7c9d429cb8c5bd680