1 citations · 2 across the 6 of their papers we have counts for
6 papers
An Anisotropic Onsager Criterion for the Two-Dimensional Navier--Stokes Equations with Horizontal Viscosity
Siyu Liang
We consider distributional weak solutions of the two-dimensional Navier--Stokes equations with horizontal viscosity on or , withou…
Uniqueness of invariant measures for stochastic damped anisotropic Navier--Stokes equations
Siyu Liang
We study a two-dimensional Navier--Stokes system with anisotropic viscosity, linear damping term, and an additive noise on the whole space . For this model we prove u…
An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning
Lukas Gonon, Arnulf Jentzen, Benno Kuckuck +3
The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of meth…
On White Noise Solutions of mSQG Equations on
Siyu Liang
In this paper, we show existence of white noise solutions for weak formulations of modified Surface Quasi-Geostrophic (mSQG) equations. Based on previous results (\cite{FS}) on whi…
A Lower Bound Estimate of Life Span of Solutions to Stochastic 3D Navier-Stokes Equations with Convolution Type Noise
Siyu Liang
In this paper we investigate the stochastic 3D Navier-Stokes equations perturbed by linear multiplicative Gaussian noise of convolution type by transformation to random PDEs. We ar…
Determinstic and stochastic 2d Navier-Stokes equations with anisotropic viscosity
Siyu Liang, Ping Zhang, Rongchan Zhu
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-posednes…