28 citations · 97 across the 35 of their papers we have counts for
19 papers · 1 filter
Characterisations for the depletion of reactant in a one-dimensional dynamic combustion model
Siran Li, Jianing Yang
In this paper, a novel observation is made on a one-dimensional compressible Navier--Stokes model for the dynamic combustion of a reacting mixture of -law gases () with dis…
On analysis of the exponential map of volume-preserving diffeomorphism group on closed orientable surfaces through the vorticity
Siran Li
We study the exponential map of group of volume-preserving diffeomorphisms on closed orientable surfaces via the vorticity formulation of the incompressible Euler equation. We pres…
On Asymptotic Rigidity and Continuity Problems in Nonlinear Elasticity on Manifolds and Hypersurfaces
Gui-Qiang G. Chen, Siran Li, Marshall Slemrod
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this…
Fractional Sobolev isometric immersions of planar domains
Siran Li, Mohammad Reza Pakzad, Armin Schikorra
We discuss regularity and developability of isometric immersions of flat domains into enjoying a local fractional Sobolev regularity for $2/3…
A new proof of the Gaffney's inequality for differential forms on manifolds-with-boundary: the variational approach à la Kozono--Yanagisawa
Siran Li
Let be a compact Riemannian manifold-with-boundary. We present a new proof of the classical Gaffney's inequality for differential forms in boundary value spaces…
A Note on Alberti's Luzin-Type Theorem for Gradients
Siran Li
We give a "soft" proof of Alberti's Luzin-type theorem in [1] (G. Alberti, A Lusintype theorem for gradients, J. Funct. Anal. 100 (1991)), using elementary geometric measure theory…
-maps with positive distributional Jacobians
Siran Li, Armin Schikorra
We extend the well-known result that any , with strictly positive Jacobian is actually continuous: it is also true for fracti…
Towards a Theory of Multi-Parameter Geometrical Variational Problems: Fibre Bundles, Differential Forms and Riemannian Quasiconvexity
Siran Li
We are concerned with the relaxation and existence theories of a general class of geometrical minimisation problems, with action integrals defined via differential forms over fibre…
Counterexamples to the -Calderón--Zygmund Estimate on Open Manifolds
Siran Li
Based on a construction due to B. Güneysu and S. Pigola (\textit{Adv. Math.} \textbf{281} (2015), pp.353--393), for each and , we exhi…
The Inviscid Limit of the Navier-Stokes Equations with Kinematic and Navier Boundary Conditions
Gui-Qiang G. Chen, Siran Li, Zhongmin Qian
We are concerned with the inviscid limit of the Navier-Stokes equations on bounded regular domains in with the kinematic and Navier boundary conditions. We first est…
From the Nash--Kuiper Theorem of Isometric Embeddings to the Euler Equations for Steady Fluid Motions: Analogues, Examples, and Extensions
Siran Li, Marshall Slemrod
Direct linkages between regular or irregular isometric embeddings of surfaces and steady compressible or incompressible fluid dynamics are investigated in this paper. For a surface…
Geometric Regularity Criteria for Incompressible Navier--Stokes Equations with Navier Boundary Conditions
Siran Li
We study the regularity criteria for weak solutions to the incompressible Navier--Stokes equations in terms of the geometry of vortex structures, taking into account the bound…
On the Existence of Isometric Immersions of Several Classes of Negatively Curved Surfaces Into
Siran Li
We prove the existence of isometric immersions of several classes of metrics on surfaces into the three-dimensional Euclidean space , wher…
On Vortex Alignment and Boundedness of Norm of Vorticity
Siran Li
We show that the spatial () norm of the vorticity of an incompressible viscous fluid in or remains bounded uniformly in time, provided…
Regularity of Desingularised Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach
Siran Li
We establish the regularity of weak solutions for the vorticity equation associated to a family of desingularised models for vortex filament dynamics in 3D incompressible viscous f…
Dimension Reduction of Compressible Fluid Models over Product Manifolds
Siran Li
In this paper we study the dimension reduction limits of the compressible Navier--Stokes equations over product Riemannian manifolds $\mathcal{O}_ε\cong \mathcal{M} \times ε\mathca…
On one-dimensional compressible Navier-Stokes equations for a reacting mixture in unbounded domains
Siran Li
In this paper we consider the one-dimensional Navier-Stokes system for a heat-conducting, compressible reacting mixture which describes the dynamic combustion of fluids of mixed ki…
Global Weak Rigidity of the Gauss-Codazzi-Ricci Equations and Isometric Immersions of Riemannian Manifolds with Lower Regularity
Gui-Qiang G. Chen, Siran Li
We are concerned with the global weak rigidity of the Gauss-Codazzi-Ricci (GCR) equations on Riemannian manifolds and the corresponding isometric immersions of Riemannian manifolds…
Fluids, Elasticity, Geometry, and the Existence of Wrinkled Solutions
Amit Acharya, Gui-Qiang Chen, Siran Li +2
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonl…