21 citations · 55 across the 13 of their papers we have counts for
13 papers
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs
Ke Chen, Chunmei Wang, Haizhao Yang
Deep neural networks (DNNs) have achieved remarkable success in numerous domains, and their application to PDE-related problems has been rapidly advancing. This paper provides an e…
Global well-posedness of the 1d compressible Navier-Stokes system with rough data
Ke Chen, Ly Kim Ha, Ruilin Hu +1
In this paper, we study the global well-posedness problem for the 1d compressible Navier-Stokers system (cNSE) in gas dynamics with rough initial data. Frist, Liu- Yu (2022) establ…
Low-rank approximation for multiscale PDEs
Ke Chen, Shi Chen, Qin Li +2
Historically, analysis for multiscale PDEs is largely unified while numerical schemes tend to be equation-specific. In this paper, we propose a unified framework for computing mult…
Global Calderón--Zygmund theory for parabolic -Laplacian system: the case
Ke Chen, Quoc-Hung Nguyen, Na Zhao
The aim of this paper is to establish global Calderón--Zygmund theory to parabolic -Laplacian system: $$ u_t -\operatorname{div}(|\nabla u|^{p-2}\nabla u) = \operatorname{div} (…
The Peskin problem with initial data
Ke Chen, Quoc-Hung Nguyen
In this paper we study the Peskin problem in 2D, which describes the dynamics of a 1D closed elastic structure immersed in a steady Stokes flow. We prove the local well-posedness f…
The Muskat problem with data
Ke Chen, Quoc-Hung Nguyen, Yiran Xu
In this paper we prove that the Cauchy problem of the Muskat equation is wellposed locally in time for any initial data in .