4 papers · 1 filter
A brief introduction to the regularity theory of minimising harmonic maps
Siran Li
We introduce various classical, foundational results on the regularity theory of harmonic maps, with focuses on the energy minimising harmonic maps. Topics include inner and outer…
On well-posedness theory of very weak solutions to Navier-Stokes equations on irregular domains with nonhomogeneous Dirichlet boundary data
Xiaojin Bai, Siran Li, Xiangxiang Su
The well-posedness theory of very weak solutions is a central topic in mathematical hydrodynamics, especially in the regularity theory for Navier-Stokes equations. It has been full…
Spacetime decay of mild solutions and conditional quantitative transfer of regularity of the incompressible Navier--Stokes Equations from to bounded domains
Siran Li, Xiangxiang Su
We are concerned with the "transfer of regularity" phenomenon for the incompressible Navier--Stokes Equations (NSE) in dimension ; that is, the strong solutions of NSE on…
Some recent developments on isometric immersions via compensated compactness and gauge transforms
Siran Li
We survey recent developments on the analysis of Gauss--Codazzi--Ricci equations, the first-order PDE system arising from the classical problem of isometric immersions in different…