4 papers
Sharp Asymptotic Stability of Blasius Profile in the Steady Prandtl Equation
Hao Jia, Zhen Lei, Cheng Yuan
This work presents an asymptotic stability result concerning the self-similar Blasius profiles of the stationary Prandtl boundary layer equation. Initially dem…
Sampling via Föllmer Flow
Zhao Ding, Yuling Jiao, Xiliang Lu +2
We introduce a novel unit-time ordinary differential equation (ODE) flow called the preconditioned Föllmer flow, which efficiently transforms a Gaussian measure into a desired targ…
Backward Uniqueness for 3D Navier-Stokes Equations with Non-trivial Final Data and Applications
Zhen Lei, Zhaojie Yang, Cheng Yuan
Presented is a backward uniqueness result of bounded mild solutions of 3D Navier-Stokes Equations in the whole space with non-trivial final data. A direct consequence is that a sol…
Deep Neural Network Approximation of Composition Functions: with application to PINNs
Chenguang Duan, Yuling Jiao, Xiliang Lu +2
In this paper, we focus on approximating a natural class of functions that are compositions of smooth functions. Unlike the low-dimensional support assumption on the covariate, we…