6 papers
A low regularity exponential-type integrator for the derivative nonlinear Schrödinger equation
Lun Ji, Hang Li, Alexander Ostermann
In this work, we present a first-order unfiltered exponential integrator for the one-dimensional derivative nonlinear Schrödinger equation with low regularity. Our analysis shows…
Liouville-type theorems for the stationary non-Newtonian fluids in a slab
Jingwen Han, Han Li
In this paper, we investigate Liouville-type theorems for stationary solutions to the shear thickening fluid equations in a slab. We show that the axisymmetric solution must be tri…
Quantum machine learning for efficient reduced order modelling of turbulent flows
Han Li, Yutong Lou, Dunhui Xiao
Accurately predicting turbulent flows remains a central challenge in fluid dynamics due to their high dimensionality and intrinsic nonlinearity. Recent developments in quantum algo…
Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schrödinger equation
Hang Li, Xicui Li, Katharina Schratz +1
We propose and rigorously analyze a novel family of explicit low-regularity exponential integrators for the nonlinear Schrödinger (NLS) equation, based on a time-relaxation framew…
Physics-Informed Neural Networks for the Korteweg-de Vries Equation for Internal Solitary Wave Problem: Forward Simulation and Inverse Parameter Estimation
Ming Kang, Hang Li, Qiwen Tan +5
Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equa…
The existence of a bounded linear extension operator for when
Han Li
Let denote the homogeneous Sobolev-Slobodeckij space. In this paper, we demonstrate the existence of a bounded linear extension operator from the jet space…