9 papers
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…
Existence of semiglobal -isometric immersions for negatively curved surface metrics with unbounded second fundamental form
Siran Li
This paper is concerned with the existence theory of isometric immersions of surfaces with negative Gaussian curvature into the three-dimensional Euclidean space. We reformulate th…
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…
A compensated compactness theorem for pseudodifferential operators on vector bundles
Siran Li, Xiangxiang Su, Yuantu Zhu
We establish a compensated compactness theorem in the microlocal and geometric analytic framework. For a weakly -convergent sequence of sections of a vector bundle o…
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…
On local solubility of Bao--Ratiu equations on surfaces related to the geometry of diffeomorphism group
Siran Li, Xiangxiang Su
We are concerned with the existence of asymptotic directions for the group of volume-preserving diffeomorphisms of a closed 2-dimensional surface within the full diffeomorp…
On the fundamental theorem of submanifold theory and isometric immersions with supercritical low regularity
Siran Li, Xiangxiang Su
A fundamental result in global analysis and nonlinear elasticity asserts that given a solution to the Gauss--Codazzi--Ricci equations over a simply-connected closed…
A smooth isotopy of volume-preserving diffeomorphisms on unit cube saving energy through extra dimensions
Siran Li
We construct an explicit example of a smooth isotopy of volume- and orientation-preserving diffeomorphisms on () that has infinite total…