7 papers
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…
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…
Nematic-Isotropic phase transition in Beris-Edward system at critical temperature
Xiangxiang Su
We are concerned with the sharp interface limit for the Beris-Edward system in a bounded domain in this paper. The system can be described as the incompress…
A wedge product theorem of compensated compactness theory with critical exponents on Riemannian manifolds
Xiaojin Bai, Siran Li, Xiangxiang Su
We formulate and prove compensated compactness theorems concerning the limiting behaviour of wedge products of weakly convergent differential forms on closed Riemannian manifolds à…